Inverse Trigonometric Functions Calculator

Want to calculate the angle value of the inverse trigonometric function? Try our inverse trigonometric functions calculator to evaluate the angle of inverse trigonometric function.

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Table of Contents:

Introduction to Inverse Trigonometric Functions Calculator:

Inverse trigonometric functions calculator is an online tool that helps you to find the angle value of the inverse trigonometric function problem. It is used to compute the angle of the inverse trigonometric function of cosine, sine, and tangent function problems in a few seconds.

Inverse Trigonometric Functions Calculator with Steps

Our tool helps students, teachers, and professionals make notes, assignments, or projects related to an inverse trigonometric function without any error quickly and easily.

What is Inverse Trigonometric Functions?

Inverse trigonometric function is defined as the ratio of the trigonometric function that is used to find the angle θ value. There are three basic functions of trigonometrics which means we have the inverse of a trigonometric function.

These inverse trigonometric functions are arccos(x), arctan(x), and arcsec(x). The inverse trig functions are known as arc functions. It is used to find the angle of a right-angle triangle from any trigonometric function. It is used in various fields like geometry, engineering, physics, etc.

How to Calculate the Inverse Trigonometric Functions?

To calculate inverse trigonometric functions, some steps are involved in the functionality of the inverse trig calculator and these steps can provide you information about manual calculation. Let's see the calculation method of the inverse function with steps.

Step 1:

The inverse trigonometric functions calculator identifies the given inverse trigonometric function angle value θ first.

Step 2:

Choose the appropriate inverse trigonometric function as per your given input value from the given function that is given below:

  1. Inverse Sine (arcsin or sin-1)

Find the angle value θ in radians or degrees, and put it into the given function as sin⁡(θ) = x.

$$ sin⁡(θ) \;=\; x $$

$$ θ = sin^{-1}(x) $$

  1. Inverse Cosine (arccos or cos-1)

Find the angle value θ in radians or degrees of a cosine function, put it into the given cosine function as cosine⁡(θ) = x is equal

$$ cosine⁡(θ) \;=\; x $$

$$ θ \;=\; cosine^{-1}(x) $$

  1. Inverse Tangent (arctan or tan-1)

To find the tangent angle value θ in radians or degrees, put it into the given function as tan⁡(θ) = x.

$$ tan(θ) \;=\; x $$

$$ θ \;=\; tan^{-1}(x) $$

The above solution of inverse function solver with steps describes the whole process of inverse trigonometric function.

Example of Inverse Trigonometric Functions:

The inverse trig functions calculator can help you to compute the inverse trigonometric functions, but it is important for you to understand it manually. So here is a practical example that gives you a better understanding of its calculation process.

Example:

Solve the triangle in the given figure for the angle θ.

PASTE THE DIAGRAM HERE!

Solution:

$$ cos⁡(θ) \;=\; x $$

$$ x \;=\; \frac{9}{12} $$

$$ cos \theta \;=\; \frac{9}{12} $$

$$ \theta \;=\; cos^{-1} \left(\frac{9}{12} \right) $$

$$ \theta \approx 0.7227 $$

How to Use Inverse Trig Calculator?

Inverse trig functions calculator has a simple design that enables you to find the angle value of the inverse trigonometric function. Before the calculation process in the inverse trigonometric functions calculator follows some simple steps. These steps are:

  1. Enter the angle value of the required inverse trigonometric function in the input box.
  2. Review your angle value before hitting the calculate button to start the evaluation process in the inverse trig function calculator.
  3. Click the “Calculate” button to get the result of your given angle value problem for the inverse trigonometric function.
  4. You should try out the calculator with trig inverse, if you have doubts about the trigonometric inverse calculator solution then you can use the load example so that you get an accurate solution.
  5. Click on the “Recalculate” button to get a refresh page for the evaluation of more solutions of inverse trigonometric function questions.

Outcome of Inverse Trig Functions Calculator:

The calculator with inverse trig calculator gives you the solution as per the given questions when you add the input value to it. It may contain as:

  • Result Option:

The result option of inverse trig solver gives you a solution for the inverse function problem to get a solution.

  • Possible Steps:

It provides you with a solution where all the evaluation processes are mentioned in a stepwise method for the inverse trigonometric function problem.

Benefits of Using Calculator with Trig Inverse:

Inverse trig solver provides many advantages whenever you use it to find the inverse trigonometric questions to get solutions immediately. These benefits are:

  • Calc inverse trig functions is a handy tool that allows you to get the solution to different kinds of inverse trigonometric function questions with a solution.
  • Our tool gives a facility you can use to get solutions of more examples related to this concept.
  • Inverse trigonometric functions calculator is a free tool therefore you can use it to find the inverse trigonometric function question in real time without spending any fee.
  • This calculator provides you with the solution in a complete process in a stepwise method so that you get clarity on its procedure.
  • Our tool saves you time and effort from doing inverse trigonometric question calculations and provides the solution as per your given input question.
  • The inverse trig function calculator is an easy-to-use tool so you can use it anywhere through any electronic device.
Related References
Frequently Ask Questions

How to differentiate inverse trigonometric functions?

To differentiate the inverse trigonometric functions we use the specific differentiation rules for each function. For inverse function differentiation, the direct formula of derivation is used such as:

Function: y = sin−1(x)

Differentiate the function with respect to x,

$$ \frac{dy}{dx} \;=\; \frac{1}{\sqrt{1 - x^2}} $$

Function: y = cos−1(x)

Differentiate the function with respect to x,

$$ \frac{dy}{dx} \;=\; - \frac{1}{\sqrt{1 - x^2}} $$

Function: y = tan−1(x)

Differentiate the function with respect to x,

$$ \frac{dy}{dx} \;=\; \frac{1}{\sqrt{1 + x^2}} $$

Which inverse trigonometric function has a range of 0 pi?

The inverse trigonometric function that has a range of [0,π] is the arccosine function, denoted as cos⁡−1(x). It means that if you input a value x into the arccosine function, the output y will be an angle that falls within the interval from 0 to π radians (or 0∘, 180∘).

The arccosine function specifically has a range of [0,π], which makes it unique in this respect among the inverse trigonometric functions.

Can you use the chain rule on inverse trigonometric functions?

Yes, you can use the chain rule on inverse trigonometric functions just as you did with any other functions. The chain rule is a process in differentiation that allows you to find the derivative of a composite function. Here’s how to apply the chain rule to inverse trigonometric functions.

$$ \frac{dy}{dx} \;=\; f’ (g(x)) . g’(x) $$

Do inverse trigonometric functions have cofunction identities?

Yes, the inverse trigonometric functions do have cofunction identities, though they might not be as commonly discussed as the cofunction identities for regular trigonometric functions. Cofunction identities are used to find the functions that are evaluated at complementary angles, and they can be extended to inverse trigonometric functions as well.

For example inverse trigonometric function and its cofunction identity which is arcsine and arccosine. For complementary angles, where the sum of the angles is π/2, the identities are:

$$ sin^{-1} (x) + cos^{-1} (x) \;=\; \frac{\pi}{2} $$

Is a trigonometric equation the same as an inverse function?

No, the trigonometric equation is not the same as an inverse function. The trigonometric equation involves trigonometric functions in which the objective is to find the values of the angle (variable) that satisfy the equation. While the inverse trigonometric function is specifically used to find the angle whose trigonometric function has a given value.

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