Lesson 4 Summary

 

There is no limit to the number of possible trigonometric identities. In this lesson you focused on a set of related identities: the sum, difference, and double-angle identities. You also saw that it is often possible to predict an identity from previous knowledge.

 

Sum Identities	Difference Identities
sin (A + B) = sin A cos B + cos A sin B	sin (A − B) = sin A cos B − cos A sin B
cos (A + B) = cos A cos B − sin A sin B	cos (A − B) = cos A cos B + sin A sin B

 

Double-Angle Identities
sin 2A = 2 sin A cos A	cos 2A = cos2A − sin2A
	cos 2A = 2 cos2A − 1
	cos 2A = 1 − 2 sin2A

 

Identities are useful when you are interested in changing the form of an equation or expression; you simply exchange one side of the identity for the other. Remember, if your identity has a restricted domain, that restriction will carry on to the equation or expression if the identity is used.

 

In the next lesson you will learn how to prove a trigonometric identity and, more importantly, why you would want to do that.