Math 1316
Section 5.6 Class Notes
Half-Angle Identities
Example 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
Find 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 trigonometric function.
33.
1  cos 400
2
35.
1  cos1470
1  cos1470
41. 
1  cos 8
1  cos 8
Verify 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