Inverse functions and trigonometric equations

The trigonometric functions take an angle and give a number. Often we need to go backward: given the number, find the angle. This chapter defines the inverse trigonometric functions, which do exactly that.

It then solves trigonometric equations. Because these functions repeat, an equation like ${\sin x=\dfrac12}$ has infinitely many solutions, and we will learn to find them all.

This chapter covers the following topics:

Inverse trigonometric functions

The inverse sine, cosine, and tangent functions, their graphs, exact values, and expressions such as ${\cos(\sin^{-1}x)}$.

Trigonometric equations

Finding all solutions of equations like ${\sin x=\dfrac{1}{2}}$, equations with multiple angles, and equations solved by factoring.

Equations that use identities

Using identities to rewrite an equation in one function, squaring both sides, and applications.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.