# How to Solve Inverse Trig Functions

2021-5-17

The inverse trigonometric functions are the inverse functions of the trigonometric functions in mathematics. However, under certain conditions, you have to restrict the domain values. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to determine the angle measure when at least two sides of a right triangle are known. Inverse trigonometric functions are widely used in many scientific fields including engineering, navigation, physics, and geometry. Read the blog to master the methods of how to solve inverse trig functions.

## Review inverse functions in general

By reviewing the general inverse function can help you build a stronger foundation of trigonometry before stepping into solving inverse trig functions. If you want to find the inverse of a function, just replace all the x’s with y’s and all the y’s with x’s. So if you want to find the inverse of y=sin x, you can flip the variables and get x=sin y.

Then you can solve this equation for y by taking inverse sine (sin^-1 or arcsin) of both sides because the sin^-1 and the sin will cancel on the right side. Sin^−1 and arcsin both indicate the inverse of the sin function and can be used interchangeably. You can use whichever notation you’re comfortable or more familiar with unless your professor requires you to use one of them consistently. The fact is, both of them are used very frequently, so you should be aware that they mean the same thing.

## Inverse trig function explained

You might sometimes feel clueless when solving inverse trig functions, let’s put it in a simpler way! Inverse trig functions act as the opposite of the regular trigonometric functions. For example:

- Inverse sine (sin^-1) does the opposite of the sine.
- Inverse cosine (cos^-1) does the opposite of the cosine.
- Inverse tangent (tan^-1) does the opposite of the tangent.

- arcsin(x), or sin^-1(x), is the inverse of sin(x)
- arccos(x), or cos^-1(x), in the inverse of cos(x)
- arctan(x), or tan^-1(x), is the inverse of tan(x)

- Arcsine
- Arccosine
- Arctangent
- Arccotangent
- Arcsecant
- Arccosecant

In general, if the trig ratio is given but the angle is asked to solve, you can use the corresponding inverse trig function to find the angle and solve the problem. More impotently, in order to define the inverse functions, it is essential to restrict the domain of the original functions to an interval where they are invertible.

Hope you have been able to understand a bit more about how to solve inverse trig functions after reading this.

## Use algebra to find an inverse function

The most efficient method of how to do inverse trig functions for a given one-to-one function involves the following steps:

- Replace the function notation’s name with y.
- Reverse all the x’s and y’s (let every x be y and every y be x).
- Solve the equation for y.
- Replace y with the function notation for an inverse function.
- Get the answer & solve the problem

## Use a scientific or graphing calculator

If you have a scientific or graphing calculator, the inverse trig functions are generally the 2nd functions of the trig buttons, which allows you to do inverse trig functions on it much easier with graphs.

The following steps are how to compute for the specific functions:

To find the inverse sine, press the keys 2nd and sin; to find the inverse cosine, press the keys 2nd and cos; to find the inverse tangent, press the keys 2nd and tan.

Reminder: make sure to set your calculator with the correct angle units upon needs: radians or degrees. Switch between them can help you achieve a more accurate calculation.

## Get help from the ultimate trig problem solver ‒ Lumist

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The Lumist app is undoubtedly one of the best apps you will encounter to help you with math problems. This app uses the camera on your phone coupled with augmented reality to solve inverse trig functions. All you need to do is to point your phone’s camera at the paper containing the equation or math problem you are looking to solve, and it will give you the answer by actually reading and recognizing the problem itself with AI Tech. It reads the problem and solves it instantly, and all you need is your device’s camera.

Explore animated homework answer videos with key concepts, crafted to increase your learning stamina with interactive Q&A features. Both Algebra 2 & pre-calculus will be supported in the app and help you master the methods of how to do inverse trig functions.

There are also tons of trigonometry video tutorials provided on Lumist youtube channel. It provides plenty of examples and practice problems such as inverse sine, cosine, and tangent functions.

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