Download y - Wsfcs

Chapter 4 Test NAME: _________________________ Date: _________
1. Convert the measure to radians.
7
revolution counterclockwise from the x-axis
10
[A]
7
5
[B]
7π
10
[C]
7π
5
[D] –252
2. In which quadrant is the terminal side of the angle θ ?
9π
θ =−
5
[A] Quadrant I
[B] Quadrant II
[C] Quadrant III
[D] Quadrant IV
3. Find one positive angle and one negative angle that are coterminal with the given angle.
π
–
3
4. Express the angle in degree measure.
π
4
5. Convert the measure from degrees to radians. Round to three decimal places.
–4°
6. The needle of the scale in the bulk food section of a supermarket is 26 cm long. Find the
distance the tip of the needle travels when it rotates 64°.
[A] 166.4 cm
[B] 14.5 cm
[C] 4.6 cm
[D] 29 cm
7. A point on the rim of a wheel has a linear speed of 18 cm s. If the radius of the wheel is
20 cm, what is the angular speed of the wheel in radians per second?
[A] 0.5 rad s
[B] 18
. rad s
[C] 2.8 rad s
1
[D] 0.9 rad s
Chapter 4 Test NAME: _________________________ Date: _________
8. A 65-foot long irrigation sprinkler line rotates around one end as shown. The sprinkler
moves through an arc of 200° in 2.2 hours. Find the speed of the moving end of the
sprinkler in feet per minute. Round your answer to the nearest tenth.
s
= 200°
r = 65 ft
9. One city is 130 miles due north of another city. Assuming that the earth is a sphere of radius
3964 miles, what is the difference in their latitudes?
10. Identify the point that lies on the unit circle.
[A]
FG 50 , 23IJ
H 73 73K
[B]
FG 4 , 3IJ
H 5 5K
[C]
FG 64 , − 15 IJ
H 49 49 K
[D]
FG − 16 , − 25IJ
H 41 41K
11. The length of an arc along a wheel which has a radius of 1 foot is found by wrapping a tape
π
measure around the wheel. What is the arc length that corresponds to a central angle of ?
9
b
g
12. If the point 0.72, y is on the unit circle in Quadrant I, what is the value of y ? Round to
three decimal places.
2
Chapter 4 Test NAME: _________________________ Date: _________
13. Use the coordinates of a point on the unit circle to write the trigonometric ratio.
b x, yg
b0, 1g
t
b1, 0g
b g
tan − t
14. Identify the trigonometric function as an even function or an odd function.
y = sec θ
15. Identify the ratio that defines the trigonometric function of the angle θ .
cosθ
c
a
b
[A]
c
a
[B]
a
b
[C]
c
b
[D]
b
c
16. Find the exact value of the six trigonometric functions of the angle θ given in the figure.
(Use the Pythagorean Theorem to find the third side of the triangle.)
50
14
3
Chapter 4 Test NAME: _________________________ Date: _________
17. Use the fundamental trigonometric identities to determine the simplified form of the
expression.
cot ß sin ß
[A] cos ß
[B] csc ß
[C] sec ß
[D] tan ß
18. Use the fundamental trigonometric identities to determine a simplified form of the
expression.
cos2 ß
1 − sin 2 ß
19. Let θ be an acute angle. Use the given function value and trigonometric identities to find the
indicated trigonometric function.
5
If cos θ = , find sin θ .
6
20. Use a calculator to evaluate the function. (Be sure the calculator is in the correct angle
mode.)
csc 68° 13′ 49″
[A] 1.0768
[B] –12.2528
[C] –1.2924
[D] 0.9287
21. The cable supporting a ski lift rises 2 feet for each 5 feet of horizontal length. The top of the
cable is fastened 1320 feet above the cable’s lowest point. Find the lengths b and c, and find
the measure of angle θ .
c
1320 ft
b
[A] b = 528 ft
c = 1422 ft
θ = 68.2°
[B] b = 3300 ft
[C] b = 1422 ft
c = 3554 ft
θ = 218
.°
c = 528 ft
θ = 0.4°
4
[D] b = 3554 ft
c = 3300 ft
θ = 23.6°
Chapter 4 Test NAME: _________________________ Date: _________
22. A 20-foot ladder makes an angle of 62° with the ground as it leans against a wall. How far
up the wall does the ladder reach?
[A] 22.65 ft
[B] 17.66 ft
23. Given tan θ = −
[A] cos θ = −
[C] 9.39 ft
[D] 37.61 ft
8
and sin θ < 0, find cos θ .
5
5 89
89
[B] cos θ = −
8 89
89
[C] cos θ =
8 89
89
[D] cos θ =
5 89
89
24. The point given is on the terminal side of an angle in standard position. Find the cotangent,
the secant, and the cosecant of the angle.
– 3, 4
b
g
Find the reference angle θ ′.
25. θ =
8π
15
26. θ = – 3.4
[A] −
22 π
15
[A] 0.2584
[B]
7π
15
[C]
[B] 2.8832
22 π
15
[C] 18292
.
[D] −
[D] – 3.4
27. Find the indicated trigonometric value in the specified quadrant.
3
θ is in Quadrant II and cos θ = − . Find sin θ .
8
28. Give the number of full cycles of the function that are found in the interval.
y = 2 sin x on the interval – 5π, 11π
[A] 9
[B] 8
[C] 7
29. List the key points on the graph of the function.
y = 4.5 cos x on the interval 0, 2 π
30. Sketch the graph of the function.
y = 2.5 sin x on the interval – 2 π, 2 π
5
7π
15
[D] 16
Chapter 4 Test NAME: _________________________ Date: _________
31. Find the amplitude and the period of the function.
x
y = – 15
. cos
2
[A] Amplitude = 15
.
1
Period =
2
[B] Amplitude = 15
.
Period = 4 π
[C] Amplitude = – 15
.
1
Period =
2
[D] Amplitude = – 15
.
Period = 4 π
32. List the start and end points of any full cycle on the graph of the function.
y = 2 sin 6 x + 5π
b
g
33. Sketch the graph of the function.
y = 2.5 sin 4 x − 6π − 1 , on the interval – 2 π, 2 π
b
g
34. A weight attached to the end of a spring is pulled down 3 centimeters below its equilibrium
point and released. It takes 5 seconds for it to complete one cycle of moving from
3 centimeters below the equilibrium point to 3 centimeters above the equilibrium point and
then returning to its low point. Identify the sinusoidal function that best represents the
position of the moving weight and the approximate position of the weight at 8 seconds.
bg
[A] h t = 5 cos
bg
2 πt
, 4.3 cm
3
bg
[C] h t = –3 cos
[B] h t = –5 sin
bg
2 πt
, 2.4 cm
5
[D] h t = 3 sin
2 πt
, – 2.5 cm
3
2 πt
, 2.4 cm
5
35. The high and low tides of a coastal city on May 3, 2000 are shown in the table. Find an
equation for h t , the height of the water as a function of t, the number of hours after
midnight. Assume that the water height can be modeled by a cosine function. If needed,
round to three decimal places.
bg
Tide
Time
High 3:00
Low 9:12
Height
A. M.
101 cm
A. M. 41 cm
6
Chapter 4 Test NAME: _________________________ Date: _________
36. Identify the function that is graphed.
y
5
4
3
2
1
–1
–2
–3
–4
–5
− 2π
[A] y = − cot
2π
x
4
x
[B] y = − tan 4 x
[C] y = tan
x
4
[D] y = cot 4 x
37. Sketch the graph of the function and write equations for 2 consecutive asymptotes.
5x 5π
y = − tan
+
4 16
FG
H
IJ
K
38. Identify the equation that matches the description of the function.
5π
8π
.
A secant function has a phase shift of −
and a period of
4
3
FG 3x − 15π IJ
H 4 16 K
F 8x 15π IJ
y = sec G +
H 3 16 K
FG 3x − 5π IJ
H4 4K
F 3x 15π IJ
y = sec G +
H 4 16 K
[A] y = sec
[B] y = sec
[C]
[D]
39. Give the period and the phase shift of the function.
5x 5π
y = – 15
. sec
−
4
8
FG
H
IJ
K
40. What is the damping factor in the equation?
bg
f x =e
− x2 3
sin 3x
7
Chapter 4 Test NAME: _________________________ Date: _________
41. Use a calculator to approximate the expression.
arccos − 0.2
b g
[A] 1.57
[B] 1.77
[C] 1.02
8
[D] 1.00
Reference: [4.1.2.5]
[1] [C]
Reference: [4.1.2.6]
[2] [A]
Reference: [4.1.2.8]
5π
3
7π
Negative coterminal angle: –
[3]
3
Positive coterminal angle:
Reference: [4.1.3.11]
[4] 45°
Reference: [4.1.3.12]
[5] –0.070
Reference: [4.1.4.13]
[6] [D]
Reference: [4.1.4.14]
[7] [D]
Reference: [4.1.4.15]
. ft min
[8] 17
Reference: [4.1.4.16]
[9] 1° 52′ 44 ″
Reference: [4.2.1.17]
[10] [B]
Reference: [4.2.1.19]
[11] 0.35 ft
Reference: [4.2.1.20]
[12] 0.694
Reference: [4.2.2.24]
y
−
[13] x
Reference: [4.2.3.28]
[14] even function
Reference: [4.3.1.33]
[15] [D]
Reference: [4.3.1.35]
14
48
14
48
50
50
sin θ = ; cosθ = ; tan θ = ; cot θ = ; sec θ = ; csc θ =
[16]
50
50
48
14
48
14
Reference: [4.3.2.38]
[17] [A]
Reference: [4.3.2.39]
[18] Answers may vary. Sample answer: 1
Reference: [4.3.2.40]
[19]
11
6
Reference: [4.3.3.41]
[20] [A]
Reference: [4.3.4.45]
[21] [B]
Reference: [4.3.4.46]
[22] [B]
Reference: [4.4.1.49]
[23] [D]
Reference: [4.4.1.52]
3
5
5
cot θ = − , secθ = − , csc θ =
[24]
4
3
4
Reference: [4.4.2.53]
[25] [B]
Reference: [4.4.2.54]
[26] [A]
Reference: [4.4.3.60]
[27]
sin θ =
55
8
Reference: [4.5.1.61]
[28] [B]
Reference: [4.5.1.63]
Fπ I
0, 4.5g , G , 0J , b π,
b
H2 K
[29]
g FGH 32π , 0IJK
– 4.5 ,
Reference: [4.5.1.64]
y
5
2π x
– 2π
–5
[30]
Reference: [4.5.2.65]
[31] [B]
Reference: [4.5.3.71]
FG
H
Answers may vary. Sample answer: −
[32]
Reference: [4.5.3.72]
y
5
4
3
2
1
− 2π
[33]
–1
–2
–3
–4
–5
Reference: [4.5.4.74]
[34] [C]
2π
x
IJ FG
KH
IJ
K
5π
π
, 0 , − , 0
6
2
Reference: [4.5.4.76]
bg
b
g
.
+ 71
[35] h t = 30 cos 0.507 t − 1520
Reference: [4.6.1.78]
[36] [C]
Reference: [4.6.1.79]
Answers may vary. Sample answer: x =
y
5
4
3
2
1
–1
–2
–3
–4
–5
− 2π
[37]
2π
Reference: [4.6.3.85]
[38] [D]
Reference: [4.6.3.88]
8π
π
period = , phase shift =
[39]
5
2
Reference: [4.6.4.91]
[40] e − x
2
3
Reference: [4.7.2.97]
[41] [B]
x
3π
13π
, x= −
20
20