Download 5.5 Double Angle Identities Double Angle

5.5 Double Angle Identities Double Angle Identities 
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sin 2
cos 2
cos 2
cos 2
tan 2
2 sin cos 2
1
1 2
Examples: Use Identities to find values of the sine and cosine functions for each angle. 1. , given cos 2
and terminates in quadrant I. 0 and sin
0 since is in quadrant I. 1 Solution: Both cos
cos 2
2
2
2
1 1 1 1
1
√
sin
√
cos
√
√
cos
sin
√
√
2. , given cos 2
2
2
cos
cos
. 0 and sin
0 since is in quadrant II. 1 Solution: cos
cos 2
2
and 1 1 1 1
1
√
sin
√
√
√
√
√
√
sin
√
√
√
√
√
3. 2 , given cos
0 and sin
Solution: cos 2
2
1 cos 2
2
1 cos 2
2
1 1 2
2
2
2
1 1 1 2
1
sin 2
sin 2
4. Express sin 4 as a trigonometric function of x. Solution: sin 4
sin 2 2 2 sin 2 cos 2 2 2 sin cos
4 sin cos x
4
sin
4 sin cos Verify the identities: 5. sin 2
·
Solution: 6. sec 2
sec 2 2 sin cos
sin 2