 # Inverse Trigonometric Functions

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Examples, solutions, videos, worksheets, games, and activities to help PreCalculus students learn about the inverse trigonometric functions: inverse sine function, inverse cosine function, and inverse tangent function and also how to solve problems using the three inverse trigonometric functions.

An Introduction to Inverse Trigonometric Functions

Using inverse trig functions to determine an angle. Solve right triangles.
Introduction to the inverse functions of sine, cosine, and tangent.
Define inverse functions of sine, cosine, and tangent.
Graph the inverse functions of sine, cosine, and tangent.
Use inverse trigonometric functions to solve problems.

Inverse Sine Function
Since sine is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted sine function. The inverse sine function is written as sin-1(x) or arcsin(x). Inverse functions swap x- and y-values, so the range of inverse sine is -pi/2 to pi/2 and the domain is -1 to 1. When evaluating problems, use identities or start from the inside function.

How to restrict the domain of sine so it will have an inverse function? Inverse Cosine Function
Since cosine is not a one-to-one function, the domain must be limited to 0 to pi, which is called the restricted cosine function. The inverse cosine function is written as cos-1(x) or arccos(x). Inverse functions swap x- and y-values, so the range of inverse cosine is 0 to pi and the domain is -1 to 1. When evaluating problems, use identities or start from the inside function.

How to restrict the domain of cosine so it will have an inverse function? Inverse Tangent Function
Since tangent is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted tangent function. The graph of the inverse tangent function is a reflection of the restricted tangent function over y = x. Note that the vertical asymptotes become horizontal, at y = pi/2 and y = -pi/2, and the domain and ranges swap for the inverse function.

How to restrict the domain of tangent so it will have an inverse function? Evaluating Expressions Involving Inverse Sine, Inverse Cosine, and Inverse Tangent

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