PC­­Lesson 5­4(a)_notes.notebook November 16, 2015

5.4(a) Sum and Difference Formulas

Students will be able to use sum and difference formulas to evaluate trigonometric functions, verify trigonometric identities, and solve trigonometric equations.

sin(A ± B) = sinA cosB ± cosA sinB

sin(A + B) = sinA cosB + cosA sinB

sin(A ­ B) = sinA cosB ­ cosA sinB

cos(A ± B) = cosA cosB sinA sinB

cos(A + B) = cosA cosB ­ sinA sinB

cos(A ­ B) = cosA cosB + sinA sinB

Example

Find the exact value of each expression.

1. (a) sin( + ) (b) sin + sin 2π 3

5π 6

2π 3

5π 6

2. (a) cos( ­ ) (b) cos ­ cos 7π 6

π 3

7π 6

π 3

PC­­Lesson 5­4(a)_notes.notebook November 16, 2015

Example

Find the exact values of the sine and cosine of the angle.

17π 12

7π 6

π 4

= +

Example

Write the expression as the sine or cosine of an angle.

(a) sin 110o cos 80o + cos 110o sin 80o

(b) cos cos ­ sin sin 4π 9

4π 9

π 8

π 8

PC­­Lesson 5­4(a)_notes.notebook November 16, 2015

Homework

P381: 11, 13, 31, 35­41(odd)

Example

Find the exact value of the expression.

(a) cos cos ­ sin sin

(b) cos 120o cos 30o + sin 120o sin 30o

π 16

3π 16

3π 16

π 16