Aim: How do we develop and apply the formula for cos (A B)?

Do Now: Evaluate the following

1. cos (60° – 30°)

2. cos 60° cos 30° + sin 60° sin30°

3. cos(60° + 30°)

4. cos 60° cos 30° – sin 60° sin 30°

HW: p.492 # 10,12,16,18 p.495 # 10,14,16,18

Difference of two angles of cosine

cos(A – B) = cos A cos B + sin A sin B

Sum of two angles of cosine

cos (A + B) = cos A cos B – sin A sin B

Example: Find exact value of cos 75

cos 75 = cos(120 – 45) = cos 120 cos 45

+ sin 120 sin 45 = 2

2

2

3

2

2

2

1

Example: A

B

1. If Sin A = 3/5 with in quadrant II and cos B

is in quadrant I,= 5/13 with

We can use these formulas to find the exact values of non special angles

find cos (A – B).

* First of all, find cos A and sin Bcos A = – 4/5, sin B = 12/13

cos (A – B) = cos A cos B + sin A sin B = (- 4/5)(5/13) + (3/5)(12/13) = -20/65 + 36 /65 = 16/65

4

6

4

2

4

26

Example: If 3

3tan,

2

3cos

,and

, is not in quadrant I

Is not in quadrant IV

Find the value of )cos(

sinsincoscos)cos(

2

1

2

1

2

3

2

3

4

1

4

3

4

13

2

1

4

2

APPLICATION:

1. Find the exact value of cos 15°

2. Use cos (A – B) to show cos(270° – x ) = – sin x

3. If ,4

1cos,

2

1sin

BA

and both A and B are in quadrant III.

Find cos(A – B)

If ,2sec,2

3cot yx Both angles are in quadrant III.

Find the exact value of cos(x – y)

4.