Math 1316
Section 5.6 Class Notes
H alf-A ngle Identities
E xample 1: Use identities to find each exact value.
11. sin 67.5o
15. cos 165o
1
Math 1316
Section 5.6 Class Notes
14. tan 195o
F ind each of the following:
11. cos (x/2), given cos x = ¼ with 0 < x < π/2.
2
Math 1316
Section 5.6 Class Notes
20. sin (x/2), given cos = -5/8 with π/2 < x < π.
21. tan (x/2), given sin x 3/5 with 90o < x < 180o.
3
Math 1316
Section 5.6 Class Notes
Use an identity to write each expression as a single trigonomet ric function.
33.
1 cos 400
2
35.
1 cos1470
1 cos1470
41.
1 cos 8
1 cos 8
V erify each identity.
x tan x sin x
51. sin 2
2
2 tan x
4
Math 1316
55. 1 tan2
Section 5.6 Class Notes
2
2 cos
1 cos
5