MATH 58
Fall 2016
WEEKLY REVIEW #8
DUE: Thursday, November 3
NOTE: These problems are to be done on Engineering paper, using the standard homework format.
You may consult with me or with other students on this assignment. Questions about these
problems will not be answered during class.
1. Verify:
1
1
+
= 2 csc 2 x
1 + cos x 1 − cos x
2. Verify:
sec θ + cot θ
= 1 + csc θ − sin θ
sec θ
3. Find the exact value of sin (x − y) given that sin x = 13 , cos y =
1
4
, with x in Q II and y in Q IV.
5
4. Find the exact values of sin( 12 θ ) and cos( 12 θ ) when sin θ = − 13
and
3π
2
< θ < 2π .
5. Use the identity for the cosine of a sum and other identities to show that: cos(3x) = 4 cos 3 x − 3cos x .