6.4.1 sum and difference formulas

6.4 Sum and Difference FormulasUsing Sum/Difference to Find Exact Values(Angles Measured in Degrees)

Sum and Difference Formulas for Cosine

cos cos cos sin sin

cos cos cos sin sin

Use Sum Formula to find exact value cos105 cos 60 45 cos60 cos 45 sin 60 sin 45

1 2 3 2

2 2 2 2

2 6

4 4

14 2 6

Use Difference Formula to find exact valuecos105 cos 135 30

cos135 cos30 sin135 sin30

2 3 2 1

2 2 2 2

6 2

4 4

14 2 6

Sum and Difference Formulas for Sine

sin sin cos cos sin

sin sin cos cos sin

Use Sum Formula to find exact value sin 75 sin 30 45

sin 30 cos 45 cos30 sin 45

1 2 3 2

2 2 2 2

2 6

4 4

14 2 6

Use Difference Formula to find exact valuesin 75 sin 120 45

sin120 cos 45 cos120 sin 45

3 2 1 2

2 2 2 2

6 2

4 4

14 6 2

Sum and Difference Formulas for Tangent

tan tantan

1 tan tan

tan tantan

1 tan tan

Hint: Always use one angle whose reference angle is 60⁰ instead of 30⁰

Use Sum Formula to find exact value tan195 tan 135 60 tan135 tan 60

1 tan135 tan 60

1 3

1 1 3

1 3

1 3

1 3

1 3

4 2 3

1 3

4 2 3

2

2 3

Use Difference Formula to find exact valuetan195 tan 240 45

tan 240 tan 45

1 tan 240 tan 45

3 1

1 3 1

3 1

1 3

1 3

1 3

4 2 3

1 3

4 2 3

2

2 3

Find the Exact Value

sin 65 cos 25 cos65 sin 25

sin cos cos sin

sin

sin 65 25

sin 90

1

Find the Exact Value

cos 40 cos 20 sin 40 sin 20

cos cos sin sin

cos

cos 40 20

cos 601

2

ASSIGNMENT

p. 481 # 2 - 8, 13 - 16, 21 - 26