Math 111 Test 2
1. The measure of an angle is 130◦ . Find the measure of the angle in radians.
(a)
(b)
(c)
(d)
(e)
13
18
13
−
18
13π
18
13π
−
18
3π
−
4
2. The length of a arc is 6 and the radius of the circle is 10, find the measure of the central
angle.
(a)
3
5
3◦
5
3π
5
5π
−
3
5
−
3
5◦
−
3
(b) −
(c)
(d)
(e)
(f)
3. Find the area of the sector of a circle of radius 2 formed by angle of 30◦ .
(a) 60
(b) 60◦
π
(c)
3
π◦
(d) −
3
1
(e) −
3
1◦
(f) −
3
1
4. Find the exact value of the expression cos
3
3
√
3−2 3
6
√
2−1
2
√
√
2−2 3
2
√
2+1
2
√
√
2+2 3
2
(a) 1 −
(b)
(c)
(d)
(e)
(f)
√
5. Find the exact value of tan
!
17π
2
π
π
− tan
4
3
"
(a) 1
1
(b)
2
1
2
(d) −1
(c) −
(e) Does not exist
√
6. The point (− 23 , 12 ) is on the terminal side of an angle θ in the standard position on the unit
circle. Find the exact value of sin θ
√
3
(a) −
2
1
(b)
2
(c) 2
√
3
(d)
2
√
(e) − 3
√
(f) 3
7. Find exact value of cos 5π.
(a) 1
(b) −1
(c) Does not exist
(d) 2
(e) −
3
2
2
8. Find the exact value of the expression:
− cos2 (20◦ ) − tan2 (380◦ ) cos2 (20◦ )
(a) 1
(b) −1
(c) −2
(d) 2
(e) Does not exist
Problems (9) and (10), refer to the following information: sin θ =
3
5
and tan θ < 0.
9. Which Quadrant is θ in?
(a) I
(b) II
(c) III
(d) IV
10. What is the exact value of cos θ?
4
(a)
5
4
(b) −
5
4
(c)
3
4
(d) −
3
3
(e) −
4
11. What is the equation of a sine function that has amplitude 2 and period 6?
(a) 2 sin(3x)
(b) 2 sin(3πx)
(c) 2 sin( π3 x)
(d) −2 sin(6x)
(e) −2 sin(3πx)
12. What is the phase shift of y = −2 cos(5x − π)?
(a)
π
2
π
2
π
(c) −
5
π
(d)
5
(e) π
(b) −
3
13. Match the function y = 2 sin( π2 x) to the correct graph
4
14. Write an equation for the graph below
(a) 2 sin( π2 x)
(b) −2 sin( π2 x)
(c) 2 sin( π2 x) + 1
(d) 2 sin( π3 x) − 1
(e) 2 sin( π2 x) − 1
15. Write an equation for the graph below
(a)
(b)
(c)
1
2
1
3
1
2
cos(2πx)
cos(2πx)
cos(3πx)
(d) 3 cos(2πx)
(e) None of above
5
16. Which of the following expressions is NOT correct
(a) 1 + tan2 (10) = sec2 (10)
(b) csc2 (20) − cot2 (20) = 1
(c) sin(100) = tan(100) cos(100)
(d) sin2 (23) + cos2 (24) = 1
(e) sin(15) cos(15) tan(15) cot(15) sec(15) csc(15) = 1
17. Which if the following function has the given characteristics: amplitude: 3, period: 3π, and
phose shift: 3
(a) −3 sin(2x + 1)
(b) 3 cos(x − 3π)
(c) −3 sin( 23 x − 2)
(d) 3 sin( 23 x + 2)
(e) −3 cos( 23 x + 2)
18. If cos θ = − 35 and
π
2
< θ < π, find the value of tan θ.
3
5
4
−
3
3
−
4
4
3
5
3
5
4
(a) −
(b)
(c)
(d)
(e)
(f)
19. If sin θ = − 35 and sec = 54 , find the value of tan θ.
3
5
4
−
3
3
−
4
4
3
3
4
5
4
(a) −
(b)
(c)
(d)
(e)
(f)
6
20. What is the domain of the tangent function
(a) All real number
π
2
(c) All real number except integer multiplies of π
π
(d) All real number except integer multiplies of
2
(e) None of above
(b) All real number except odd multiplies of
7
KEY
1. c
2. a
3. c
4. d
5. e
6. b
7. b
8. b
9. b
10. b
11. c
12. d
13. f
14. e
15. e
16. d
17. c
18. b
19. c
20. b
8