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

Double-Angle Formulas

Ditch the 2s in sin 2x and cos 2y

8.1    Express sin 2x as a product of single-angle trigonometric functions.

The expression sin 2x is described as a “double angle,” because the argument of the expression is 2x rather than simply x. The identity below allows you to rewrite the double-angle expression sin 2x as the product of two single-angle expressions.

sin 2x = 2 sin x cos x

8.2    Verify your answer to Problem 8.1 by applying the sum formula for sine.

Apply the sum formula for sine to expand sin 2x. Note that sin 2x = sin (x + x).

This formula comes from Problem 7.34.

8.3    Simplify the expression: .

Apply the double-angle ...

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