Warm UpEvaluate each of the following.

1) cos (150 ○) 2) sin (360 ○)3)

4) 5) 6)

6

11cos

4

5sin

3

2sin

6

17sin

7) tan(240○) 8) csc(-225○)

9) cot(20π/3) 10) sec(- π/4)

Sum, Difference, Double and Half Angle

Identities

• Use your calculator to approximate cos75°.–Make sure you’re in Degree Mode!

• Does cos(30°+45°) = cos30° + cos45°?

Sum/Difference Identities(You need to MEMORIZE these)

• cos(A + B) = cosA cosB - sinA sinB • cos(A - B) = cosA cosB + sinA sinBExamplesCalculate:

1. Cos75° 2. Sec75°

(You need to MEMORIZE these) • sin(A + B) = sinA cosB + cosA sinB • sin(A - B) = sinA cosB - cosA sinBExamplesCalculate:

1. Sin(7π/12)

2. Csc(7π/12)

Practice

Example:Calculate

(You need to MEMORIZE these)

More Examples

Half Angle Identities…(You do not have to memorize these)

1 coscos

2 2

A A

1 cossin

2 2

A A

sintan

2 1 cos

A A

A

Use the half angle identity to evaluate…

1. tan(π/8) 2. sin(105°)