**Functions of Multiple Angles**

Instead of cos x = 1, solve cos 5x = 1

*Note: In Problems 10.33–10.36, you solve similar equations, each with a different coefficient of x. In each problem, identify all solutions on the interval 0 ≤ x < 2π.*

**10.33** Solve the equation: sin *x* + 1 = 0.

Subtract 1 from both sides of the equation to isolate sin *x* left of the equal sign.

sin *x* = –1

Taking the arcsine of both sides of this equation solves it for *x*.

*x* = arcsin (–1)

Note that the range of arcsine is –π/2 ≤ arcsin *x* ≤ π/2, so if you were asked to supply the exact solution to this equation, the answer would be *x* = –π/2. However, the problem directs you to identify all solutions within a single rotation on the coordinate plane. The only angle on this interval ...

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