Download Math 102: Trigonometry Test 3 Winter, 2016 Dr. Matsumoto

Math 102: Trigonometry
Test 3 Winter, 2016
Dr. Matsumoto
Name___________________________________
Each multiple-choice question is worth 2 points without partial credit. Other questions are worth 5 points each unless
otherwise specified.You may NOT use a calculator on this test.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write in terms of the co-function of a complementary angle.
1) sin 24°
A) csc 156°
B) cos 156°
C) cos 66°
Use trigonometric identities to find the exact value.
2) sin 20° cos 100° + cos 20° sin 100°
1
3
A) B)
2
2
3)
C)
1
3
D) csc 66°
D) -
3
2
tan 10° + tan 20°
1 - tan 10° tan 20°
A)
1
2
B) 2
C)
3
3
D)
3
Use an identity to write the expression as a single trigonometric function or as a single number.
1 + cos 6°
4)
2
A) sin 3°
B) cot 3°
C) cos 3°
1
D) tan 3°
Determine whether or not the function is one-to-one.
5)
y
4
-8
-4
4
8
x
-4
A) Yes, one-to-one.
B) Not one-to-one.
Find the exact value of the real number y.
3
6) y = sin-1
2
A)
2π
3
7) y = arccos A) -
π
4
8) y = tan-1 (-1)
π
A) 4
B)
π
3
C)
3π
4
D)
π
4
B)
7π
4
C)
π
4
D)
3π
4
B)
7π
4
C)
3π
4
D)
5π
4
2
2
2
Evaluate the expression. (You may want to draw pictures.)
9) sin (arctan 2)
2 5
A) 2 5
B)
5
10) csc sin-1
A)
5 2
2
D) 5 2
C)
3
4
D)
3
5
3
5
B)
4
3
Answer each question.
Use identities to find the indicated value for each angle measure.
4
11) cos 2θ = and θ is in quadrant I
Find sin θ.
5
12) sin θ = -
C)
4 3π
,
< θ < 2π
5
2
Find cos(2θ).
3
5
3
Verify that each equation is an identity.
13) (1 + tan2 x )(1 - sin2 x ) = 1
14) csc x - sin x = cos x cot x
4
Find the exact value of the expression using the provided information.
1
1
15) Find tan(s + t) given that cos s = , with s in quadrant I, and sin t = - , with t in quadrant IV.
3
2
Use Identities to find the exact value.
16) cos 165°
Find the exact value by using a sum or difference identity.
17) sin(-15°)
5
Find the exact value by using a half-angle identity.
18) sin
22.5°
Determine all solutions of the equation in radians.
x
1
π
19) Find cos , given that cos x = and x terminates in 0 < x < .
2
4
2
Provide an appropriate response.
20) Show, by giving an example, that the statement sin-1 (sin x) = x is FALSE for some real number x. (All you need
is one counterexample.)
6
Solve the equation for the interval [0, 2π).
21) cos2 x + 2 cos x + 1 = 0
22) 2 sin 2 x = sin x
23) sec (2x) = 1 - tan (2x)
7
Solve the equation for all real solutions.
24) 2 sin2 x + sin x = 1
Solve the equation for all real solutions.
1
25) sin x cos x =
2
Solve the equation for all real solutions.
26) sin x + cos x = 2
8