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dCode

Tool / solver to resolve one or more trigonometric equations, equations with unknown variables and cos, sin, tan, etc.

Trigonometric Equation Solver - dCode

Tag(s) : Symbolic Computation

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  • Trigonometric Equation Solver
  • Mathematics
  • Symbolic Computation
  • Trig Equation Solving

Answers to Questions (FAQ)

  • What is a trigonometric equation?

A trigonometric equation is a mathematical expression with an equality between two elements containing unknown variables and trigonometric functions (cos, sin, tan, etc.).

Example: $ \cos(x) = sin(\pi) $

  • How to solve a trigonometric equation?

dCode automatically solves the trigonometric equations (with the = equality symbol) and calculates the values of the unknowns.

All trig functions are supported: sin() , cos() , tan() , but also the trigonometry reciprocal functions acos() , arcsin() , and so on. as well as the hyperbolic functions cosh() , sinh() , etc.

Example: $ \sin(x) = 0 $ returns the solution $ x = 0 $ (radian)

Some equations will have an infinite number of solutions (modulo $ \pi $ or $ 2\pi $ or with constants $ c_i $)

All angles are in radian.

  • How to solve multiple trigonometric equations?

Multiple trig equations with the same variables can be combined with a logical AND operator: && or ⋀ .

Also, any new line return will be considered as a new equation.

  • How to solve a trig equation step by step?

The dCode solver does not display the calculation steps because they do not reflect the steps of a human thinking but to the steps of a machine thinking (bit-by-bit binary calculation operations) far from a hand-held resolution. dCode allows you to check a result.

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Trigonometric equations online calculator

The general form of trigonometric equation is

f ( trig ( x ) ) = 0

where - some arbitrary function, trig ( x ) - some trigonometric function.

As a rule, to solve trigonometric equation one need to transform it to the simplier form which has a known solution. The transformation can be done by using different trigonometric formulas .

For example, consider the solution of trigonometric equation

By using the cosine double angle formula, transform this equation to the simplier one:

The received equation is the very simple and has known solution. Our online calculator, build on Wolfram Alpha system is able to solve more complex trigonometric equations with step by step solution.

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Trig Triangle Calculator

Right triangle trigonometry, using two sides for right triangle trigonometry calculation, using one angle and one side for right triangle trigonometry calculation, using area and one side for right triangle trig calculation, other trigonometry and triangle calculators.

If you're dealing with trigonometry and right triangles, this trig calculator for right triangles is here for you. This tool uses trigonometry to calculate these triangles, as long as you know:

  • Two of its sides;
  • One angle and one side; or
  • The area and one side.

To learn more, keep reading this article that briefly discusses the trigonometry behind right triangles.

This trig triangle calculator uses the following widely-known trigonometric ratios, which relate the sides of a right triangle to its angles:

🙋 To know how to calculate or evaluate the sine, cosine, and tangent functions, visit our trig calculator .

Additionally, we can use the inverse trigonometric functions to solve for the angles if we know the length of the sides:

🙋 To know how to calculate or evaluate these inverse functions, visit our inverse sine , inverse cosine , and inverse tangent calculators .

Let's use the following triangle to explain how this calculator solves for the different sides and angles according to the information known.

Right triangle sides and angles

Finding the third side

If you know two sides, the easiest way to find the third side is by using the Pythagorean theorem ( what is the Pythagorean theorem ).

  • Given a and b: c = a 2 + b 2 c = \sqrt{a^2 + b^2} c = a 2 + b 2 ​ ;
  • Given a and c: b = c 2 − a 2 b = \sqrt{c^2 - a^2} b = c 2 − a 2 ​ ; and
  • Given b and c: a = c 2 − b 2 a = \sqrt{c^2 - b^2} a = c 2 − b 2 ​ .

Finding the angles

Then, we can find α \alpha α or β \beta β by taking any of the inverse trigonometric functions mentioned previously:

Finding the angle

The sum of the internal angles of a triangle will always be 360 ° 360\degree 360° . In a right triangle , there's a right angle ( 90 ° 90\degree 90° ) and, therefore, the sum of the other two angles ( α \alpha α and β \beta β ) will be 90 ° 90\degree 90° . Therefore:

  • Given β \beta β : α = 90 ° − β \alpha = 90\degree - \beta α = 90° − β ; or
  • Given α \alpha α : β = 90 ° − α \beta = 90\degree - \alpha β = 90° − α

Finding the two missing sides

To find the two unknown sides, you can use the angle α \alpha α and the trigonometric ratios:

Given a : c = a / sin ⁡ α c = a/{\sin{\alpha}} c = a / sin α and b = a / tan ⁡ α b = a/{\tan{\alpha}} b = a / tan α ;

Given b : c = b / cos ⁡ α c = b/{\cos{\alpha}} c = b / cos α and a = b × tan ⁡ α a = b \times {\tan{\alpha}} a = b × tan α ; and

Given c : a = c × sin ⁡ α a = c \times \sin{\alpha} a = c × sin α and b = c × cos ⁡ α b = c \times {\cos{\alpha}} b = c × cos α ;

If you know a a a or b b b , use the right triangle area formula that relates the base ( b b b ) to the height ( a a a ) and solve for the unknown side:

  • Given a: b = 2 × Area / a b = 2 \times \text{Area}/a b = 2 × Area / a ; and
  • Given b: a = 2 × Area / b a = 2 \times \text{Area}/b a = 2 × Area / b .

Once you know at least two sides, use the second section method to obtain the angles.

  • Trigonometry calculator ;
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  • Tangent ratio calculator ; and
  • Tangent angle calculator .

What's the leg measurement of a 45-45-90 triangle of 18 cm hypotenuse?

If the hypotenuse of a 45-45-90 triangle measures 18 cm, the length of any of its two legs is 9√2 cm or 12.728 cm . To get to this answer:

Take the sin of any of the 45° angles, which equals any of the legs ( a ) divided by the hypotenuse ( c ):

sin(45°) = a / c

Solve for the leg ( a ): a = c × sin(45°)

Remember that sin(45°) = 1/√2 and input the hypotenuse c = 18 cm : a = 18 cm × (1/√2) : = 9/√2 cm = 12.728 cm

What's the leg measurement of a 45-45-90 triangle of 10√5 inches hypotenuse?

If the hypotenuse of a 45-45-90 triangle measures 10√5 inches, the length of any of its two legs is 5√10 inches or 15.81 inches . To get to this answer:

You can use the formula that relates the hypotenuse ( c ) to any of the legs ( a ) of a 45-45-90 triangle: c = a × √2

And solve for the leg a :

a = c /√2 = (10√5 in)/√2 = 5√10 in = 15.81 in.

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  • Trigonometric Identities

Trigonometric Identities Calculator

Get detailed solutions to your math problems with our trigonometric identities step-by-step calculator . practice your math skills and learn step by step with our math solver. check out all of our online calculators here .,  example,  solved problems,  difficult problems.

Solved example of trigonometric identities

Starting from the left-hand side (LHS) of the identity

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete

Intermediate steps

Rewrite the sum of fractions as a single fraction with the same denominator

Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$

Combine and simplify all terms in the same fraction with common denominator $\cos\left(x\right)^2\sin\left(x\right)^2$

Since we have reached the expression of our goal, we have proven the identity

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Trig Calculator

Instructions: Use trig calculator to compute and evaluate any trigonometric expression that you provide, Please type in the trig expression you want to calculate, or a trig function you want to analyze, in the form box below.

trig math solver with steps

More about this Trig Calculator

This trig calculator will allow you to evaluate any trig expression that you provide. Make sure that you provide any valid trigonometric expression,it can be something direct like cos(pi/2), or it could be something that is not fully simplified, like sin(1/3*pi+3/4*pi).

You can also provide a trig function like sin(1/3*pi x +3/4*pi + x) and this calculator will analyze and if possible will deliver the corresponding period, frequency, etc., along with its graph .

Once a valid trig expression has been provided, all you need to do is to click on "Calculate" and all the steps of the calculation will be shown to you.

Trigonometric expressions are quite necessary, especially when you are solving triangles . Usually it is simple to reduce any trig calculation to the calculation of a few notable angles for the cosine and sine .

Trig Calculator

How to do trig calculations?

Doing a trig calculation can be a very general and broad task, that may have specific strategies that work best depending on the specific trig calculation you need to do and what trig functions are involved, but there are some general strategies that can serve you well.

What are the steps for a trig calculation

  • Step 1: Identify clearly the trig expression you want to calculate, and simplify numbers and fraction as much as you can. For example, if you have cos(1+1/2), you will first notice that 1+1/2 = 3/2, so you need actually cos(3/2)
  • Step 2: Once possible fractions and simple numbers are grouped and operated if possible, determine whether there are trig functions other than sin and cosine. If there are, express everything in terms of sine and cosine
  • Step 3: Now go through all the parts, that now involve only sine and cosine , and assess whether there are notable angles involving multiples or fractions of π
  • Step 4: Directly evaluate those expressions with notable angles that can be simplified. Those that cannot be directly simplified (if any) leave as it is, or provide an approximated ( rounded value ) of them

It is customary to leave as they are expressions that do not have known, simple simplifications. For example, cos(1/4) does not have simple reduction, so it is typically left as it is. But for example, cos(π/3) = 1/2, so such simple reductions are obviously carried out

Trigonometry calculator with steps

The advantage of this calculator is that it will show you all the relevant steps of the process. The process is simple: it is about simplifying expressions that only involve numbers, fractions and overall directly evaluable numeric expressions.

Then, and only then you should go for the trig calculation, so to clear up things as much as possible before attempting any trig calculation. For specific functions, you may want try this sin calculator , that uses the specific characteristics of the sine function.

Advantages of using a trigonometric calculator app

You may think, oh well, I know pretty well my trig functions for basic notable angles, so I don't need a trig calculator app. That may well be the case, though you may hesitate a bit you get presented with something like \(\sin\left(\displaystyle\frac{345}{11}\pi\right)\)....can you simplify it? Is it a notable angle?

It is truly a good thing to try to solve things by hand, and by exercising your trigonometric memory, but a trig calculator app can help you at the very least to check your answers.

 Trigometric Calculator

Example: Trig Calculation

Calculate the trig expression: \(\sin\left(\frac{5}{4}\pi\right)\)

Solution: The following trigonometric expression has been provided to be calculated:

By inspecting the given trigonometric expression, we can find one notable angle, which is \(\sin\left(\frac{5\pi{}}{4}\right)\).

▹ For the angle \(\frac{5\pi{}}{4}\) we graphically get:

 Trigometric Calculator

The trigonometric expression given can be simplified as:

Conclusion: We conclude that \(\displaystyle \sin\left(\frac{5\pi}{4}\right) = -\frac{1}{2}\sqrt{2} \approx -0.7071\).

Example: Using the trig calculator

Reduce : \(\displaystyle \cos\left(\frac{1}{3} + \frac{5}{4}\right)\)

Solution: Now we need to work on:

This trigonometric term can be simplified as follows:

Conclusion: It is concluded that \(\displaystyle \cos\left(\frac{1}{3}+\frac{5}{4}\right) = \cos\left(\frac{19}{12}\right) \approx -0.0125\).

Example: Trig simplification

Calculate \( \sin\left(\frac{2}{3} \times \frac{6}{5} \pi\right)+ \frac{2}{5}\cdot \cos(\frac{\pi}{4}) \).

Solution: By inspecting the given trigonometric expression, we can find one notable angle, which is \(\cos\left(\frac{\pi{}}{4}\right)\).

▹ For the angle \(\frac{\pi{}}{4}\) we graphically get:

 Trigometric Calculator

Conclusion: We conclude that \(\displaystyle \sin\left(\frac{2}{3}\cdot\frac{6}{5}\pi\right)+\frac{2}{5}\cos\left(\frac{\pi}{4}\right) = \frac{1}{5}\sqrt{2}+\frac{1}{4}\sqrt{-2\sqrt{5}+10} \approx 0.8706\).

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Last updated: April 1, 2023

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Table of Contents:

  • What is Trigonometry - Definition?
  • Trigonometry - History

Trigonometric Identities

Trigonometry table, trigonometry vs. geometry.

  • Trigonometry Calculator - How to Use With Steps?
  • Trigonometry Calculator - Example

Real-world Applications

With the help of a trigonometry calculator , you will be able to solve two trigonometric problems. You can use it to find the values of sine, cosine, or tangent and cotangent in the first part of the calculator. In the second part of the trigonometry calculator , you can calculate the triangle sides or angle of right triangle trigonometry.

This article provides you with tips on how to use a Trigonometry Calculator , what cos is in trigonometry, how to do trigonometry. In addition, you will learn what are and how to use trigonometry formulas. If you have other problems, you can also use our Trigonometric Functions Calculator , Cotangent Calculator , Tangent Calculator , and Power Reducing Calculator . Also, learn about fractions with our Fractions Calculator .

Take a look other related calculators, such as:

  • Phase shift calculator
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  • Power reducing formula calculator
  • Probability calculator 3 events
  • Segment addition postulate calculator
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What is Trigonometry – Definition?

A part of math science that deals with the specific functions of angles, degrees, and their application is trigonometry. Trigonometry’s name comes from the Greek words trigon , meaning triangle, and metron , meaning measure. We can divide it into planar (angles and distances in the plane) and spherical (angles and distances in space).

Trigonometry refers to studying the properties of a right triangle, lengths, and angles. We learn the relationships between the lengths of the sides of a right triangle. However, it also deals with waves and oscillations.

Trigonometry is not just a study of plane figures. It has a branch called spherical trigonometry that studies triangles in three-dimensional spaces. Astronomers use spherical trigonometry, but we can also use it for navigation.

Apart from what we use in pure mathematics, we can also apply trigonometry in many branches of science. There are six trigonometric relationships . Three basic ones, called Sine (sin), Cosine (cos), and Tangent (tan), together with Secant (sec), Cosecant (csc), and Cotangent (cot).

Trigonometry – History

Trigonometry occurs in ancient Babylon, Egypt, India, and China. These people knew practical geometry and some concepts that were an introduction to trigonometry. In the Rhind Papyrus (1800 BC, Egypt), among the 84 problems in algebra, arithmetic, and geometry, there are also five problems in which seqt is one of them.

We can define seqt in terms of the cotangent, meaning that the Egyptians knew the numerical relations in a triangle. The founder of modern trigonometry is considered to be the Hipparchus of Greece (around 190-120 BC). He was the first to calculate the values ​​of trigonometric functions. In the 2nd century, Ptolemy contributed to the development of trigonometry in his work Almagest.

Ptolemy was an astronomer and had to use some basics of trigonometry. The last major contribution to the development of trigonometry was the invention of a new term – logarithms by the Scottish mathematician John Napier in 1614. Logarithm tables greatly facilitated numerical computation, including compiling tables of trigonometric functions.

We can define trigonometric identity in terms of the equality of two expressions. These expressions remain accurate even when we include any values instead of general numbers. In short, these identities connect trig functions when math expressions need to be simplified.

Basic trigonometric identities are:

  • Connection of sine and cosine: sin 2 α+cos 2 α=1
  • Sine and tan connection: sin 2 α=tg 2 α / 1+tg 2 α
  • Cosine and tan connection: cos 2 α=1 / 1+tg 2 α

To learn more about trigonometric identities, see this related Sum and Difference Identities Calculator .

This table will make it easier for you to remember and easily find trigonometric numbers of basic angles (in degrees).

First of all, write all the functions in columns. In the first column, you write the angles: 0°, 30°, 45°, 60°, 90°. Fill in the sine column using the expression √x / 2.

For an angle of 0°, set x = 0 and then the value √x / 2 = √0 / 2 = 0. In the same column for the angle 30° set that x = 1 and from that follows √x / 2 = √1 / 2 = 1/2.

Likewise, for an angle of 45°, set x = 2 and it follows √x / 2 = √2 / 2. For an angle of 60°, set x = 3 and when we replace it, we get √x / 2 = √3 / 2 and for sin 90°, set x = 4 and when we replace it, we get the following √x / 2 = √4 / 2 = 1.

Then we fill in the column that belongs to the cosine. Fill it using the reverse order because the rule sin x° = cos (90-x)° applies.

We fill in the column that starts with a tangent. It is easy because we know that tanα = sinα / cosα. Fill in the column belonging to the cotangent in the reverse order. Learn about cofunctions, with this related Cofunction Calculator .

Mathematics has three main branches, called Arithmetic, Algebra, and Geometry . Geometry is the study of the shapes, sizes, and properties of a space of a certain number of dimensions. The geometry we can categorize as planar geometry, solid geometry, and spherical geometry.

Geometry is used daily, almost everywhere, and by everyone. You can find geometry in physics, engineering, architecture, and many others. So, we ask ourselves, what is trigonometry in geometry?

Geometry is the main branch of math, while trigonometry is the branch of geometry. Geometry is the study of the elements of a figure. Trigonometry is a study of the properties of a right triangle.

Trigonometry Calculator – How to Use With Steps?

When you want to calculate the missing sides or the angles of a right triangle, the first step is to enter the values you know. It could not be a problem. You need to calculate the value you are missing and it is enough to know the following variables: one side and one angle, two sides, area, and one side.

It is essential to know that you need more familiar variables if you have the values of two triangles. When you have two triangles of the same shape, so the angles are the same, the sizes can be different. Thus, in such triangles, the cell lengths are not the same. Such a relationship is called triangle similarity. Only if the cells have the same length do the triangles coincide.

On the whole, using these steps you can solve every trigonometry problem.

Trigonometry Calculator – Example

At what angle did the sports plane fly until it reached an altitude of 2,500 m if we know that it crossed 5 km? At that height, a paratrooper jumped out of the plane. How far is the parachute landing site from the take-off point of the plane?

Additionally, here is one more example. We can do the trigonometry in the right triangle step by step. For instance, a right triangle has a side length of 8 cm, and a hypotenuse length of 15 cm. We can find the other side length with our calculator:

  • type given a side of a triangle,
  • type given hypotenuse length.

Trigonometry calculator will calculate the next:

  • the b side will be 12.689 cm length,
  • angle α is 32.231 and angle β is 57.769.

To sum up, trigonometry is used in all mathematics, and we can apply it to all other sciences and find a result for our problem. Surveyors have used it for centuries, as have military and other engineers. We can use it in optics and statics and in physical chemistry in physics.

Trigonometry has its application in music, more precisely in computer music and modern architecture. Beautifully curved surfaces of stone and glass would be impossible without it.

The trigonometry of a right triangle can also use in aerial control. Air traffic control employees at small airports have to determine the height of the clouds in the evening. Triangle trigonometry has applications for finding unknown lengths and measuring angles in images, movies, and television. There is an ideal distance from which to look to create the best possible picture from the eye.

Some of the reasons people use angles in everyday life are position, direction, precision. Crossings on the street are usually performed as close as possible to an angle of 90°, possibly even higher, so that visibility when turning is as high as possible.

Angles are also often used in sports. Athletes who try to throw balls at certain distances, such as baseballs, basketball, soccer balls, and golf balls, strategically use angles. If they want to hit a short and high ball, they will search for an angle close to 90°. It is now clear what trigonometry is in the real world.

What are the 6 basic trigonometric functions?

Six basic trig functions are: sine, cosine, tangent, cotangent, secant, and cosecant.

Is trigonometry hard to learn?

More than two thousand years ago, people used trigonometry when adults had less knowledge than today’s high school students. So, with a greater effort, it is possible to explore this area of science at a basic level. With the professional help of a teacher or this calculator, you can also master complex tasks.

How to learn Trigonometry?

Lectures at school and independent work will help you master how to do trigonometry and understand many systematic processes. Remember that learning math is learning a particular way of thinking, not just memorizing formulas. Before learning trigonometry, learn the basics of algebra and geometry. You cannot learn trigonometry by automatic memorization. You need to understand the basic ideas and methods.

Who invented trigonometry?

Trigonometry occurs in ancient Babylon, Egypt, India, and China. The founder of modern trigonometry is Hipparchus of Greece (around 190-120 BC). He was the first to calculate the values of trigonometry functions.

When do you learn trigonometry?

At the age of 14-15, you learn how to do trigonometry. Also, you learn what is cos in trigonometry and all the basics. Advanced trigonometry you can learn at the age of 17-18.

What grade do you learn trigonometry?

In 9th grade, we learn what Trigonometry is. Now you have also this Trigonometry Calculator for you to learn more.

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Problem Solver Subjects

Our math problem solver that lets you input a wide variety of trigonometry math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

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Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

  • Long Arithmetic
  • Rational Numbers
  • Operations with Fractions
  • Ratios, Proportions, Percents
  • Measurement, Area, and Volume
  • Factors, Fractions, and Exponents
  • Unit Conversions
  • Data Measurement and Statistics
  • Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

  • Variables, Expressions, and Integers
  • Simplifying and Evaluating Expressions
  • Solving Equations
  • Multi-Step Equations and Inequalities
  • Ratios, Proportions, and Percents
  • Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

  • Algebra Concepts and Expressions
  • Points, Lines, and Line Segments
  • Simplifying Polynomials
  • Factoring Polynomials
  • Linear Equations
  • Absolute Value Expressions and Equations
  • Radical Expressions and Equations
  • Systems of Equations
  • Quadratic Equations
  • Inequalities
  • Complex Numbers and Vector Analysis
  • Logarithmic Expressions and Equations
  • Exponential Expressions and Equations
  • Conic Sections
  • Vector Spaces
  • 3d Coordinate System
  • Eigenvalues and Eigenvectors
  • Linear Transformations
  • Number Sets
  • Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

  • Algebra Concepts and Expressions Review
  • Right Triangle Trigonometry
  • Radian Measure and Circular Functions
  • Graphing Trigonometric Functions
  • Simplifying Trigonometric Expressions
  • Verifying Trigonometric Identities
  • Solving Trigonometric Equations
  • Complex Numbers
  • Analytic Geometry in Polar Coordinates
  • Exponential and Logarithmic Functions
  • Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

  • Operations on Functions
  • Rational Expressions and Equations
  • Polynomial and Rational Functions
  • Analytic Trigonometry
  • Sequences and Series
  • Analytic Geometry in Rectangular Coordinates
  • Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

  • Evaluating Limits
  • Derivatives
  • Applications of Differentiation
  • Applications of Integration
  • Techniques of Integration
  • Parametric Equations and Polar Coordinates
  • Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

  • Algebra Review
  • Average Descriptive Statistics
  • Dispersion Statistics
  • Probability
  • Probability Distributions
  • Frequency Distribution
  • Normal Distributions
  • t-Distributions
  • Hypothesis Testing
  • Estimation and Sample Size
  • Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

  • Polynomials and Expressions
  • Equations and Inequalities
  • Linear Functions and Points
  • Systems of Linear Equations
  • Mathematics of Finance
  • Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

  • Introduction to Matrices
  • Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

  • Unit Conversion
  • Atomic Structure
  • Molecules and Compounds
  • Chemical Equations and Reactions
  • Behavior of Gases
  • Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

  • Static Equilibrium
  • Dynamic Equilibrium
  • Kinematics Equations
  • Electricity
  • Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

  • Step By Step Graphing
  • Linear Equations and Functions
  • Polar Equations

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Trigonometry Calculator: A New Era for the Science of Triangles

Mathematics is definitely among the top fears of students across the globe. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics.

Why is that, you may ask? Well, it depends.

First, our educational system is lacking in terms of intuitive and interactive learning.

How do you expect the students to enjoy studying a particular subject if they don’t even like the sessions?

Although there are some exceptions, most math teachers don’t (or maybe can’t) offer active lessons. Students, especially nowadays, prefer interaction, not passive learning. But who’s to blame here, really? Teachers are that way because their teachers were that way, and the same goes for those, in a continuous loop of flaws that govern the system.

On the other hand, students don’t appreciate math enough to give it their best. There’s always the question “When am I ever going to use this in real life?”, especially when it comes to specific math branches such as algebra and trigonometry.

Little do they know that a deeper understanding of mathematics as a subject can help them have a better understanding of your environment and the world around us. Math is the primary factor responsible for ameliorating your critical thinking and improving your problem-solving skills in your adulthood.

As a general rule of thumb, people who think mathematically are much faster thinkers than others who take a creative or artistic approach whenever they need to solve a problem.

While math lovers are more realistic and thoughtful, art lovers tend to live the moment and forget about the future and what it has to offer.

What is Trigonometry?

Trigonometry is the study of the properties of triangles, mainly the relationship between the angles and the length of the different sides.

Triangles are probably one of the most basic geometrical figures . Despite that, trigonometry has unveiled numerous applications with many practical, real-life uses, including, but not limited to, estimating bearings and accurate distances.

To validate calculations and perform operations, three fundamental functions are used in trigonometry: cosine, sine, and tangent. Essentially, the sin cos tan calculator on this page can help you here. Basically, if you know the measurements of two sides or angles, you can easily determine the measures of the rest.

When you say trigonometry, you say Pythagorean theorem; a formula that’s used to calculate the length of the different sides of a triangle.

In a triangle, the hypotenuse refers to the longest side, which faces the right angle. The remaining sides are known as the perpendicular and the base.

The Pythagorean theorem can be resumed in H²= B²+P², where H refers to the hypotenuse, B to the base, and P to the perpendicular (duh!).

Many formulas or identities can be derived from the theorem, which we will detail below.

If you have a hard time wrapping your head around those concepts, don’t worry, as our trig calculator can help you make these calculations a lot faster and easier.

Pythagorean Identities in Trigonometry

All trigonometric derivations and values are based on the Pythagorean Identities . While they may seem hard to memorize and understand, they’re actually quite the opposite, as you only need to practice them in a few questions to get the gist of them. Once you do that, applying these identities in different problems will become a piece of the pie.

There are 6 fundamental identities that you must learn for you to master trigonometry. These identities can prove useful in a handful of situations, be it inside or outside the school, and they are:

  • sin²+cos²= 1² (note that 1 squared = 1)
  • tan² + 1² = sec²
  • cot² + 1² = cosec²
  • tan = sin/cos = 1/cot
  • sin = tan/ sec = 1/ cosec if you put it simply it implies that sin equals divided cosec
  • cosec = 1/sec = cot/cosec

As with any other subject, it’s all about practice, so make sure to spend even as little as 30 minutes every day solving trigonometry problems if you want to master this subject. If you find an obstacle that you can’t bypass on your own, try our trigonometry calculator online to practice and familiarize yourself with the calculations.

Why Should You Learn Trigonometry?

Despite the widespread belief that math rules can only be used in school and during exams, mathematics , specifically trigonometry, has various real-life applications in nearly any industry such as business development, physics, design, etc.

Having a hard time believing that? Here’s a couple of the non-math related career paths in which you can find a great use for your trigonometrical skills.

Music and Trigonometry

As weird as that may seem, music is actually related to math. But, how?

To put it simply, sound travels in waves that resemble the graphical representation of the cosine and sine functions . In other words, what you hear every day while you’re going to school is nothing but a mere real-life representation of these trigonometric functions. I mean, how cool is that?

Using a trigonometry calculator sin cos tan allows engineers and producers to manipulate sound by altering sound wave patterns for different variables such as treble, volume, and base to get tunes that appeal to the listeners.

You’re probably familiar with T-pain and autotune. The well-known American rapper and singer reported that he has STUDIED autotune for a couple years before starting to use it in his music.

Video Games and Trigonometry

Take a look at games like Battlefield, Call of Duty, Far Cry, and God of War, and you’ll notice that they’re becoming more realistic with every release. The shadows, motion effects, graphics rendering, and all other elements of the game have never been better.

Why are we witnessing such amelioration? Because the developers are giving their best to improve physics engines, graphic, software, and programming by focusing on the properties of trigonometry. Mind blowing, huh?

In other words, if you’re into game development and want to get a career within that field, it’s time to start practicing math and trigonometry.

Space and Trigonometry

Have you ever watched a rocket launch? No? Then go check them out on YouTube, they’re astonishing.

Trigonometry is of the utmost importance when it comes to sending equipment, such as rockets and satellites, to outer space, as such operations require precise calculations of speed and bearings. The slightest miscalculation in this field can yield catastrophic results and failures, and even the loss of human lives, so there’s no room for mistakes.

So, if working alongside Elon Musk is a fantasy of yours, you better start practicing some trigonometry.

Digital Imaging and Trigonometry

We live in a digital world, where everything is governed by creative visuals, and when it comes to those, no one can deny the importance of trigonometry.

Digital imaging is what’s behind computers and visuals, and it’s all about measurements, calculations , and geometric patterns that determine how every pixel is displayed on your screen.

In other words, if you want to dive into the world of digital imaging and creativity in the years to come, you can’t ignore math and trigonometry.

Modern Architecture and Trigonometry

Every structure, curve, and calculation in modern architecture is precisely determined using different mathematical formulas, including trigonometric ones. Do you think those skyscrapers in Dubai got to the clouds on their own? No, you silly. They’re the result of countless hours of calculations and measurements.

Interior Design and Trigonometry

Just like architecture, interior design is also ruled by mathematical and trigonometric formulas that determine what fits where and whatnot to deliver a harmonic design all over the place.

So, there they are, some career paths that are governed by trigonometry despite not being directly related to mathematics. If you want a job in any of the mentioned fields, you have no choice but to give your best and study for your math classes.

How to Learn Trigonometry?

As hard as it may seem, learning trigonometry can actually be fun. All you need is a bit of determination and dedication, and you’re already ahead of 99% of students.

If you want to learn trigonometry the right way, you can follow this simple blueprint to success:

1.   Start With Simple Concepts

From the tiny acorn, grows the mighty oak, and from simple concepts, grow the bigger theorems. Start your journey towards trigonometry mastery by studying and practicing simple concepts to familiarize yourself with the basics. These include the six major identities mentioned above and their simple applications, along with the Pythagorean theorem and its uses.

2. Practice Deriving

Once you get the gist of the basics, you need to start practicing derivation . That way, you won’t have to memorize every single identity or formula, as you’ll be able to derive them on your own. Do that repeatedly, and derivation and identities will become second nature in no time.

Practice Different Types of Problems

Once you master derivation, you need to go further by moving to more complicated problems. That way, not only will you be able to memorize formulas, but you’ll understand how to pass from one concept to the other and how to employ each one of them without breaking a sweat.

3.Keep Practicing

Do you know how to perform addition and subtraction? Of course, you do. You’ve been doing it your whole life. So, if you want trigonometry to become second nature as well, you need to practice it continuously a following a preside studying plan. We highly recommend distributing your practice over the whole week rather than cramming several hours of studying into one day. That way, you’ll avoid boredom and get a higher studying frequency at the same time.

4. Organize Study Groups

When you’re in a group, you always try to give your best to avoid showing up as the weakest, which makes study groups an excellent way to give your best while practicing trigonometry. Besides, you’ll get great value out of the verbal interchange during the session.

5.if You Need Help, Don’t Hesitate to Ask

If you get stuck while you’re trying to solve a specific problem, do not hesitate to ask your teacher or instructor for help. If they’re not available, you can visit our trigon calculator as it can show you the step-by-step process that leads to every result.

Why Use the online trigonometry calculator?

There are many reasons as to why you should use our trigonometry graphing calculator. For starters, it’s extremely easy to use, and you don’t have to spend hours trying to figure out what every button does, which is the case when using a standard scientific or graphing calculator.

We highly recommend using Mathway’s trigonometry triangle calculator if:

  • You are looking for a trigonometry calculator app

We get it. You don’t want to use a graphing calculator because they’re a bit of a burden to keep carrying around. After all, why would you do so if you can simply use an app on your phone?

The problem with apps though is that they take up space on your smartphone or tablet and they can make your device a bit laggy. If you’d rather stay away from such issues, you can simply use our online tool, which is considered as the best calculator for trigonometry. Why? Because it’s compatible with any electronic device, making it superior to apps that you have to download and install. With our triangle trigonometry calculator, solving your math problems is just a few clicks away.

Also – It’s basically an online trig calculator app.

  • You need a trigonometry calculator with steps

Are you stuck and couldn’t find a way to solve that homework your teacher gave you? Can’t find a tutor to show you the way? No problem, just sign up with Mathway and let the right triangle trigonometry calculator show you how to solve any problem step by step.

Not only can SolveMathPorblems’ solve any problem you through at it, but it can also show you the steps that led to the result. That way, you can identify your mistakes and fix them so that you can improve and push your trigonometry skills to the next level.

Remember, don’t check the result until you try solving the problem and answering your questions yourself. Otherwise, you’re only cheating yourself. Math isn’t about fooling the teacher into believing that you did a great job, it’s about unveiling your mistakes and working on your flaws. That’s why we’ve got this trig calc.

  • You need a trigonometry simplify calculator

Who said math is hard? Mathematics isn’t actually about complicating things; it’s about simplifying complicated problems and breaking them down into small chunks that you can solve one step at a time. Knowing that what applies to math, in general, goes for trigonometry as well, you’ll be content to hear that our trigonometry online calculator can simplify complex problems and solve them through the easiest of ways, thus teaching you the logical process behind every solution.

  • You don’t have a scientific calculator for trigonometry

One can find himself without a scientific calculator for a variety of reasons

Why Is the Trigonometry Calculator Online?

Being an online app, not only can our Trigonometry calculator work on any device without any downloading or installation, but it can also be used anywhere, anytime. That way, you can practice problem-solving whenever you feel like it without carrying a bulky scientific calculator with you everywhere you go.

Why Is the Trigonometry Calculator Free?

There are only a few things in this world that any one of us can consider to be priceless. Knowledge is most definitely one of them. Today, students across the globe, especially in scientific fields, are in need of aid in getting a good grasp of the essential and basic skills and tools that are required for their studies.

So when it comes to anything related to math and trigonometry, we’d like to offer as much assistance as we can. In the matter that we have at hand, we think that by providing this trig calculator (with its usage guide) to all the students around the world, we’ll be able to do the least we can in our quest for bringing knowledge to everyone in the most suitable way. And, by the way, we’re giving away this trig calculator online for free.

Hopefully, your search for a free trigonometry calculator will come to an end with what we have to offer. Keep your money in your pocket and enjoy learning with our free service.

What Can a Trigonometry Calculator Do?

Basically, a whole lot of things. Some might come in with the assumption that because it is an internet service that it cannot deliver on the same level of versatility that a regular calculator does. But that would be wrong. This online trig calculator with steps can provide multiple utilities that would satisfy all your mathematical necessities, regardless of your level. Our app can work as a:

  • Analytic trigonometry calculator
  • Right angle trigonometry calculator
  • Trigonometry solutions calculator
  • Trigonometry graph calculator
  • Trigonometry equation calculator
  • Trigonometry formulas calculator
  • Spherical trigonometry calculator

It’s not just a good trig calculator; it’s the best trigonometry calculator.

Trigonometry Calculator: Symbols

If you go on and take a look at what the interface of our calculator has to offer, you’ll come to find that it encompasses a large number of symbols. Now you can see some of them in any standard calculator, but some others are specific only to our calculator.

You’ll find symbols such as the division sign, rectangular pyramid, cylinder, trapezoid, triangle, equal to or less than, square roots, exponents, fractions, absolute value , and parenthesis among other things. Because of that, we’re confident enough to say that this calculator isn’t only the best trigonometry value calculator, but also the best inverse trigonometry calculator.

The versatility that this calculator brings makes it perfect for everything from college work, homework, testing and answer verification. So let’s say you’ve got some time to spare, you can take your Smartphone out of your pocket, go to the website and hone your trigonometry skills through problem-solving. Even if you don’t have any problems at your disposal, you can choose from our pre-existing list of examples.

Using a Calculator for Trigonometry

If you go around searching for a guideline for using a calculator for trigonometry, you probably won’t have any luck in finding anything useful. We’ll try sparing you the useless search for such a thing on the internet and give you a simple explanation of how to use the calculator so you can jump right to doing your homework. Here’s how it’s done:

  • Type in your problem either through the provided symbols or by utilizing the existing examples
  • When you click on the show button, the expression that you’ve written will be displayed in the conventional mathematical form. The “?” button is available for you to click on if you find yourself struggling with a particular issue.
  • The calculator is automatically set to detect the type of problem you’re dealing with through the input that you’ve given it. But in the case of it choosing an unsuitable choice, you can always correct it manually.
  • Tap “answer” and wait for the app do its calculations
  • Once the answer is displayed, you can compare it to the solution that you came up with.

If you happen to have made a mistake, make a note of it and practice on avoiding it in the future. If you feel like you need to see the detailed steps, all you have to do is sign up for Mathway.

So, Who Made This Trigonometry Calculator?

The brilliant work that’s been done to bring this magnificent app to life comes all from the minds of the people at Mathway. It’s only here on our website to make it easy for everyone around the world to have access to it. If you’re interested in getting the full potential of this app , you’ll have to sign up. But don’t let that deter you; it’s actually pretty simple and quick. Just make sure to have your parents’ approval if you’re underage.

This is the app you need in your arsenal if you’re looking to push yourself and improve your skills in problem-solving. It’s a free and useful calculator that has all the stuff that you’ll need to solve any trigonometry problem. From sine and cosine to the fundamental Pythagorean theorem, this is the tool that you’ll want to have by your side, or, more accurately, in your pocket.

Trigonometry, which studies the measure of triangles, takes algebra to the next level. Its most well-known features include the Pythagorean Theorem and the sine, cosine, and tangent ratios. Our trig calculator can help you check problems that involve these relationships as well as many others. Simply enter your problem into this advanced calculator to see if you worked it correctly.

Not only can this advanced calculator check answers but it can also provide additional practice problems to help hone your skills in preparation for tests and quizzes. To use this feature, find the type of problem you want to practice in the Examples section. Click on the desired topic, and an example problem will appear in the calculator screen. Click the Show button to see the problem in its standard format or as a picture if applicable. Solve the problem and click Answer to see if you are right.

Quick Trig Facts

Pythagorean theorem.

\large c^2 = a^2 + b^2

Trig Ratios

\large \sin \theta \frac{opp}{hyp}

Law of Sines

\large \frac {a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Law of Cosines

\large c^2 = a^2 + b^2 - 2ab \cos C

Reference Triangles

trig references triangles

Trigonometry Tips

  • Know your formulas: Investing the time to learn the formulas, definitions, and patterns will definitely pay off. That way, when you approach a problem, you will have the tools, like this sohcahtoa calculator, you need in order to solve it. Otherwise, you may get confused, and your work can quickly digress into a jumbled mess. You can use memory tricks such as SOH CAH TOA to help you. SOH CAH TOA, sohcahtoa, is a memory aid for the trig ratios. SOH stands for Sine = Opposite over Hypotenuse, COH means Cosine = Adjacent over Hypotenuse and TOA helps you remember that Tangent = Opposite over Adjacent.
  • Take your time: As you progress into more advanced studies of mathematics, the problems become longer and more involved. Don’t let this intimidate you, and don’t be in a hurry to get done. Carefully and methodically work through each problem step by step, and you’ll eliminate a lot of careless errors.
  • Check your answers: It doesn’t do much good to practice if you’re practicing wrong, so check your answers to make sure you’re on the right track. Our trig calculator will help you with your homework, but if you have time you also want to go back and check your answers on tests and quizzes. You’ll be surprised how many mistakes you’ll catch and how many points this will save you.
  • Identify your errors: Many students end up making the same mistakes over and over again because they don’t pay attention to what went wrong when they miss a question. Mistakes are part of the learning process, but you have to identify and correct them. Every time you get a problem wrong, diligently search for your mistake and figure out what you should have done instead. If you can’t find your error, ask a teacher or friend for help. Or, sign up for Mathway, which will show you the steps to solve any problem you enter into the calculator.

How to Use the Calculator

Starting with an Example

Trigonometry Calculator Symbol Guide

trigonometry-calculator-parentheses

Note: If no index is given, it is assumed to be two and is just called a square root.

trigonometry-calculator-coordinates

Note : If no subscript (base) is given, the base is assumed to be 10.

trigonometry-calculator-right-triangles

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