Download 1) A ladder leaning against the wall makes an angle of 18 with the

MAθ Trigonometry Test 2007
1. A ladder leaning against the wall makes an angle of 18° with the wall. If the ladder is 30 feet long, how
far is the base of the ladder from the bottom of the wall?
a) 28.53 ft
b) 9.27 ft
c) 22.53 ft
d) 19.81 ft
2. Which of the following is coterminal with the angle
a) 180°
tan t =
3. If
a)
1
b) 288°
e) none of the above
3π
?
5
c) -468° d) 368°
e) none of the above
1
and sin t is negative, find the exact value of cos ( t + π ) .
2
2
−1
−2
b)
5
c)
5
d)
5
e) none of the above
5
4. A 10 in windshield wiper travels through an angle of 120°. How far does the tip travel after one swipe
(back and forth once)?
a) 104.7 in
b) 41.9 in
c) 6000 in
d) 20.9 in
e) none of the above
5. Which of the following is an accurate expression for cot θ if θ is acute?
1 − sin 2 θ
a) −
sin θ
d) −
1 − cos 2 θ
cos θ
b)
1 − sin 2 θ
sin θ
c)
1 − cos 2 θ
cos θ
e) None of the above
6. For all values of α, sin ( −α ) + sin (α ) is equal to which of the following?
a) 2
b) 2sin (α )
c) 0
d) sin ( 2α )
e) none of the above
7. Which of the following has a period of π and a phase shift of d?
a) y = tan x + d
b) y = cos 2 x + d
d) y = tan ( 2 x − 2d )
e) none of the above
c) y = cos 2 ( x − d )
⎛ 13π ⎞
⎛ 5π
⎟ + sin ⎜
⎝ 3
⎝ 6 ⎠
5 3
c)
6
8. Find the exact value of tan ⎜
a)
3
6
b)
− 3
6
⎞
⎟.
⎠
d)
−5 3
6
e) none of the above
9. For an angle θ, where cos θ < 0 and tan θ > 0 , express the reference angle θR in terms of θ.
a)
θR = π + θ
b)
θR = π −θ
d)
θ R = θ + 2π
e) none of the above
3π ⎞
⎛
sin ⎜ x −
⎟
2 ⎠
⎝
b) cos x
c) − sin x
c)
θR = θ − π
10. Expand and simplify:
a) sin x
d) − cos x
e) none of the above
11. The eyes of a basketball player are 6 ft above the floor, and the rim of the basket is 10 ft above the
floor. If the player is at the free-throw line, which is 15ft from the center of the rim, what is the angle of
elevation from the player's eyes to the center of the rim?
a) 15°
b) 26°
c) 0.26°
d) 75°
e) none of the above
12. Find exact solutions to sin 2t + sin t = 0.
I. π
II.
π
3
2π
III.
3
a) I and II only
b) I and III only
13. Find exact solutions to
c) II and III only
d) I only
5π ⎞
2
⎛π
.
sin⎜ x +
⎟=
4 ⎠ 2
⎝4
I. 2
II. 4
III. 6
a) I only
b) II only
c) III only
d) II and III only
e) I and II only
e) none of these
E
14. Find the area of
a)
300 3
d) 150
b)
ΔDEF .
150 3
20
c) 300 2
60°
e) none of the above
F
cos 2
15. Find the exact value of
a)
2
4
b)
6
4
3
5
b)
5
4
3⎞
⎛
sin ⎜ arccos ⎟ .
4⎠
⎝
5π
c)
6
17. Give the exact value of
a) −
π
3
b)
7π
6
18. Complete the following:
a)
127D18'57"
b)
1
− .
8 2
6
c)
2
3⎞
⎛
sin ⎜ arccos ⎟ .
4⎠
⎝
4
c)
5
16. Find the exact value of
a)
π
d)
2
6
e)
2
3
d)
5
5
e)
7
4
d)
2π
3
127.6775D = __ D __'__" .
127D 48'19"
c)
127D 40 '39"
4π
3
b)
7π
6
c)
11π
6
20. Convert 147.69˚ to the nearest hundredth of a radian.
a) 1.87
b) 2.58
c) 3.06
127D32 '19"
3
⎡ 3π
⎞
, 2π ⎟ for which sin x = −
.
2
⎣ 2
⎠
5π
d)
3
19. Find the exact value of x in the interval ⎢
a)
d)
d) 3.42
30
D
21. The voltage E in an electrical circuit is modeled by E = 5cos120π t where t is time measured in
seconds. Find the period.
a)
1
60
b)
1
3
c) 5
d)
π
3
22. A circle has a radius of 18.2 cm. Find the length of the arc intercepted by a central angle of 144˚ to
the nearest tenth of a centimeter.
a) 28.9 cm
23. Simplify:
a)
2 cos 2 x
b) 33.4 cm
c) 38.3 cm
d) 40.1 cm
1 + sin x
cos x
.
+
cos x 1 − sin x
b) 0
c) sin x cos x
d) 2sin x
⎛
⎝
24. What is the maximum value of y = −4sin ⎜ 2 x +
a) 6
e) 45.7 cm
b) -6
c) -14
e) none of these
π⎞
⎟ + 10 ?
3⎠
d) 14
e) none of these
[
25. Find the largest solution in the interval 0, 2π ) of cos x = cos 2 x .
a)
5π
3
b)
11π
6
c)
4π
3
d)
7π
6
e) none of these