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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