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

Sum and Difference Formulas for Sine and Cosine

Expanding things like sin (x + y)

7.34    Apply an identity to express both of the following expressions as a sum of two products: sin (x + y) and sin (xy).

Sum and difference identities allow you to rewrite a trigonometric statement whose argument is a sum or a difference. The result is usually not simpler; you transform a single trigonometric statement into a sum or difference of two products. Though these identities do not necessarily simplify an expression, they are no less important.

The argument of sin (x + y) is (x + y).

sin (x + y) = sin x cos y + cos x sin y              sin(xy) = sin x cos y – cos x sin y

Notice that the left-hand formula above contains addition signs on both sides ...

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