Trigonometric Functions Calculator

Now calculate the angle of the trigonometric functions with the help of our trigonometric functions calculator which gives a solution in just a few seconds.

Trigonometric Function:

Angle:

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Introduction to Trigonometric Functions Calculator:

The trigonometric functions calculator is an online tool that helps you to find the angle of a given trigonometric function. It uses the trigonometric or its inverse function to compute the angle of a given triangle.

Trigonometric Functions Calculator with Steps

Our trigonometric function calculatorsimplifies the process for finding complex trigonometric problems by providing quick and accurate results for various angles, whether you want to measure in degrees or radians.

What is the Trigonometric Function?

A trigonometric function is a fundamental concept in algebra because it is extensively used when you are dealing with geometric shapes and objectives. It has six basic functions that have different purposes for solving trigonometric functions.

It is a useful method for mathematics, physics, engineering, astronomy, and various other applications that have angles and periodic functions.

Types of Trigonometric Function:

There are three types of trigonometric functions and each has its own inverse trigonometric function. The trig equation calculator solves the following functions:

For sine and cosine functions:

The sine function is denoted as sin𝜃 and the cosine function is cos 𝜃.

For tan 𝜃:

The tan 𝜃 is the ratio of sine and cosine functions. You can also solve it by using a trigonometric functions calculator.

$$ tan \theta \;=\; \frac{sin \theta}{cos \theta} $$

For secant 𝜃:

It is the inverse function of the cosine trigonometric function,

$$ sec \theta \;=\; \frac{1}{cos \theta} $$

For cosectan 𝜃:

It is the inverse function of the sine function,

$$ csc \theta \;=\; \frac{1}{sin \theta} $$

For cot 𝜃:

The cot 𝜃 function is the inverse of sin 𝜃. You can also solve the equation of cot 𝜃 by using the trig function calculator.

$$ cot \theta \;=\; frac{cos \theta}{sin \theta} $$

How to Calculate Trigonometric Functions?

For calculating trigonometric functions, you must know about the definitions and properties of these trigonometric functions to find their values for a given angle. Here is a step-by-step guide on how to calculate trigonometric functions.

Step 1:

Identify the angle for which you need to calculate the trigonometric function and the unit of the given angle so that you know whether the angle value is given in degrees or radians.

Step 2:

Add the angle value in the below trigonometric functions one by one to find its solution.

Sine function:

Find the sine function value by putting the given angle value in it.

Cosine function:

Compute cos⁡ (θ), and simplify by putting the value of the angle in it.

Tangent function:

As you know tan ⁡(θ) is the ratio of sine and cosine function so add the value of cosine and sine in it.

Secant (sec⁡):

It is the inverse function of the cosine function so you just need to find the inverse value only.

Cosecant (csc):

For csc function take the inverse of the sine function value.

Cotangent (cot⁡):

To find the cotangent value you need to take the inverse of the tan function for the solution.

Step 3:

Add the value in all the trigonometric functions and find the angle of the right-angle triangle.

Practical Example of Trigonometric Function:

You can also use the trigonometric functions calculator to solve the questions of trigonometric functions. However, an example of a trigonometric function gives you a better understanding of its calculation. Here is a manual example of solving trig equations.

Example:

Find the value of 𝜃 = 30 degrees on all the trigonometric functions.

Solution:

For sine:

$$ Sin \theta \;=\; sin (30) $$

$$ sin (30) \;=\; 0.5 $$

For cosine:

$$ cos \theta \;=\; cos (30) $$

$$ cos (30) \;=\; 0.8660 $$

For tangent:

$$ tan \theta \;=\; tan(30) $$

$$ tan (30) \;=\; 0.57735 $$

For secant:

$$ sec \theta \;=\; sec (30) $$

$$ sec (30) \;=\; 1.154701 $$

For cosecant:

$$ cosec \theta \;=\; cosec (30) $$

$$ cosec (30) \;=\; 2 $$

For cotangent:

$$ cot \theta \;=\; cot (30) $$

$$ cot (30) \;=\; 1.732051 $$

You can also get this solution directly by using the trig equation solver.

How to Use Trigonometric Functions Calculator?

The trigonometric function calculator has a simple design that enables you to calculate the angle of the given triangle without any hurdle in some seconds.

Before starting the calculation process in the trig equation calculator, you must follow some simple steps. These steps are:

Enter the angle of the trigonometric function value in its required input box.
Review your angle value before hitting the calculate button of the trig function calculator to start the evaluation process.
Click the “Calculate” button to get the result of your given trigonometric function problem.
You are trying out the trigonometric equations calculator for the first time and if you have an ambiguity about its calculation process then you can use the load example so that it provides you with an accurate solution.
Click on the “Recalculate” button to get a refresh page for the evaluation of more solutions of trigonometric function questions.

Output of Trigonometric Function Calculator:

The trig equation solver gives you the solution to given trigonometric function questions when you add the input value in it. It provides you with solutions where a complete procedure is given. It may contain as:

Result Option:

The result option of the 6 trig functions calculator gives you a solution of finding the angle problem using a trigonometric function in the solution.

Possible Steps:

The trig equations calculator provides you with a solution where all the evaluation processes are mentioned in a stepwise method for the trigonometric function problem when you click the possible step button.

Advantages of Trig Equation Calculator:

The trig functions calculator provides many advantages whenever you use it to find the angle of trigonometric function questions and give solutions immediately. It provides you with results very quickly. These advantages are:

The trigonometric equations calculator is a handy tool that allows you to get the solution to different kinds of angles for trigonometric function questions.
You can try out our trig equation solver to get solutions of more examples related to the trigonometric function concept.
It is a free tool so that you can use it to find the trigonometric function question in real time without spending any fee.
The trig function calculator provides you with the solution in a complete process in a stepwise method so that you get clarity on the trigonometric function working method.
Our tool saves you time and effort in finding trigonometric angle question calculations and provides the solution quickly.
The trigonometric functions calculator is a trustworthy tool that provides you with accurate solutions whenever you use it to find out the angle of a trigonometric function without error in the solution.

Frequently Ask Questions

What is the use of trigonometric functions?

Trigonometric functions are essential methods used for finding the unknown sides or angles in triangles and for both right-angled triangles and non-right-angled triangles using the Law of Sines and the Law of Cosines in algebra calculus.

What is a function of trigonometrics are even?

In trigonometric functions, the even functions are those for which the value of the function at −x is equal to the value x at the function. A function f(x) is considered even if it satisfies the condition.

$$ f(−x) \;=\; f(x) $$

The cosine and secant functions are even functions because it satisfy the property f(−x) = f(x).

What is an odd trigonometric functions?

In algebra, the sine, tangent, cosecant, and cotangent functions are odd functions because they satisfy the property f(−x) = −f(x). This means that the function is symmetric with respect to the origin, and changing the angle to its negative value results in the negative function’s value.

In trigonometry, odd functions should satisfy the condition:

$$ f(−x) \;=\; −f(x) $$

How to add and subtract trigonometric functions?

For adding and subtracting the trigonometric functions you need to combine their values, often using trigonometric identities to simplify the expressions. Here is a step-by-step guide on how to perform these operations on trigonometric function with the help of a given example

Example: Evaluate $$ sin⁡(30∘) + cos⁡(30∘) $$

Given that

$$ sin⁡(30∘) \;=\; 0.5 $$
$$ cos⁡(30∘) \;=\; \frac{3}{2} \approx 0.866 $$
$$ sin⁡(30∘) + cos⁡(30∘) \approx 0.5 + 0.866 $$
$$ =\; 0.5 + 0.866 \;=\; 1.366 $$

Are all trigonometric functions continuous?

Yes, all trigonometric functions are continuous within their domains. However, there are some important functions like sine (sin⁡(x)) and cosine (cos⁡(x)) functions that are continuous for all real numbers.

On the other hand the tangent (tan⁡(x)), cotangent (cot⁡(x)), secant (sec⁡(x)), and cosecant (csc⁡(x)) functions have discontinuities at specific points where their respective denominators (cosine or sine) are zero.

Amanda Jepson

Last Updated February 21, 2024