O'Reilly logo

The Humongous Book of Trigonometry Problems by W. Michael Kelley

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required