Section 5.3 Double angle formulas
sin 2A = 2 sin A cos A
1. Use a double angle formula to find the exact value of tan 2A if cos A = ­3/4 and A is in quadrant 3.
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2
cos 2A = cos A ­ sin A
= 2cos2A ­ 1
= 1 ­ 2 sin2A
tan 2A =
2tan A
1 ­ tan2A
2. Prove:
cos2A = 1 + cos 2A
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EXAMPLE: Simplify the following expressions by using the double angle formulas:
a) 2cos2105o ­ 1
b) 2sin75ocos75o
Section 5.4
Half­angle identities
1.
2.
3.
4.
Now YOU try it!
1.
Find cos (A/2) when tan A = 9/40 and A is in quadrant 3.
2.
Find tan (A/2) when tan A = ­5/2, A is in quadrant 2.
Answers to student problems:
1. cos (A/2) = ­ √1/82 2. tan (A/2) =
√29 + 2
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