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INSTRUCTOR: Dr. Bathi Kasturiarachi
NAME:
Math 11022
Fall 2008
Trigonometry
REVIEW for Exam 2 { Sections (6.5, 7.1, 7.2, 7.3)
1.
Find the exact value of
arcsin(1)
2.
Find the exact value of
tan
5
4
tan sin
1
1
2
tan cos
1
2
5
tan
3.
4.
5.
1
Find the exact value of
Find the exact value of
Find an algebraic expression in terms of x for the following.
sin (arccos x)
6.
Find an algebraic expression in terms of x for the following.
!
p
x2 5
1
sec cos
2x
7.
Prove the following trigonometric identity.
1
8.
1
1
+
cos x 1 + cos x
Prove the following trigonometric identity.
sin3 + cos3
9.
(sin + cos )(1
Prove the following trigonometric identity.
tan2 x
sec x + 1
10.
2 csc2 x
1
cos x
cos x
Prove the following trigonometric identity.
(tan
11.
Find exact value of sin(195o ).
12.
Find exact value of cos(17 =12).
sec )2
1
1 sin
1 + sin
sin cos )
13.
If sin =
1
5
nd the exact values of the following.
sin(
14.
=4)
cos(
Find the exact value of
sin sin
=3)
4
5
1
tan
tan( + =6)
1
15. Find the exact value of the expression:
sin 105o
16.
Find the exact value of the expression:
sin
17.
For the angles
18.
If sin =
19.
If sin =
4
5
3
7
and
and
and
5
12
shown in the gures, nd cos( + ).
lies in quadrant III, nd sin( =2).
lies in quadrant II, nd cos( =2).
2
3
4
20.
Find the exact value of sin(2x), if cos x =
2
3
and 0o < x < 90o .
21.
Find the exact value of cos(2x), if tan x =
5
4
and x lies in quadrant III.
22.
Verify the identity:
23.
sin 4
4 sin( ) cos( ) cos(2 )
cos 4x
8 cos4 x
Verify the identity:
3
8 cos2 x + 1
24.
Express the following product as a sum.
sin 6 sin 4
25.
Express the following product as a sum.
cos 3 cos
26.
Express the following sum as a product.
sin 5
27.
sin 3
Express the following sum as a product.
cos 3 + cos 2
28.
Prove the identity:
sin 4x + sin 8x
sin 4x sin 8x
4
tan 6x cot(2x)