# Introduction to the trigonometric angle addition identities

5 videos

1 skill

Learn about the trigonometric angle addition identities, which help us discuss the trig values of sums of angles in terms of the trig values of the individual angles. For example, we can express sin(x+y) in terms of sin(x), sin(y), cos(x), and cos(y).

### Review of the trigonometric angle addition identities

VIDEO
11:07 minutes

Sal reviews all the different trigonometric angle addition identities: sin(a+b), sin(a-c), cos(a+b), cos(a-b), cos(2a), and sin(2a).

### How to use the cosine angle addition identity (example)

VIDEO
5:14 minutes

Sal evaluates the cosine of the sum of 60° and another angle whose right triangle is given. To do this, he must use the cosine angle addition formula.

### How to use the cosine double-angle identity (example)

VIDEO
3:28 minutes

Sal evaluates the cosine of twice an angle whose right triangle is given. To do this, he must use the cosine double-angle formula.

### Practice using the trigonometric angle addition identities

PRACTICE PROBLEMS

Find the trig values of sums of angles whose individual trig values are known.

### Proof of the sine angle addition identity

VIDEO
8:26 minutes

Sal proves the identity sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y).

### Proof of the cosine angle addition identity

VIDEO
6:02 minutes

Sal proves the identity cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y).