Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari,...
Transcript of Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari,...
![Page 1: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/1.jpg)
Aratari, Trigonometry: Chapter 2-Form A Name: 41
Take the Quiz!2.1
1. Graph one cycle of the pure form y = sin x and label the critical points.
–1
1
x
y
2��–2� –�
2. Graph one cycle of the pure form y = cos x and label the critical points.
–1
1
x
y
2��–2� –�
3. Find an equation of the form y = A cos x or y = A sin x that represents the graph.
a. b.
x
y
�–�
–8
–1
1
–2� 2�–2
4
x
y
2�–2�
![Page 2: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/2.jpg)
![Page 3: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/3.jpg)
Aratari, Trigonometry: Chapter 2-Form B Name: 43
Take the Quiz2.1
1. Graph one cycle of the pure form y = cos x and label the critical points.
–1
1
x
y
2��–2� –�
2. Graph y = −3 sin x on −2π ≤ x ≤ 2π . State the range and the x-intercepts.
range
x-intercepts
–3
4
1
x
y
2��–2� –�
3. Find an equation of the form y = A cos x or y = A sin x that represents the graph.
a. b.
–4
5
1
x
y
2�–2�
–3
2
x
y
2�–2�
![Page 4: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/4.jpg)
![Page 5: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/5.jpg)
Aratari, Trigonometry: Chapter 2-Form A Name: 45
Take the Quiz2.1–2.2
1. Graph at least one cycle of each of the following and label the critical points for one cycle. Fill in the blanks, ifappropriate, with the amplitude, period, x-intercepts and/or range.
a. y = −4 cos xAmplitude
Period
x-intercepts
–3
4
1
x
y
2��–2� –�
b. y = sin1
4x
Amplitude
Period
Range
x
y
![Page 6: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/6.jpg)
46 Aratari, Trigonometry: Quiz 2.1–2.2 Form A
2. Find an equation in the form y = A sin[B(x − C)], or y = A cos[B(x − C)] that represents the graph. More thanone answer is possible.
a.
–2
2
x
y
2��–2�
b.
–4� 4�
–6
6
3
x
y
–2� 2�
![Page 7: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/7.jpg)
Aratari, Trigonometry: Chapter 2-Form B Name: 47
Take the Quiz2.1–2.2
1. Graph one cycle of each of the following and label the critical points. Fill in the blanks with the amplitude, period,x-intercepts and range.
a. y = 2 sin x
Amplitude
Period
Range
x-intercepts
–3
4
1
x
y
2��–2� –�
b. y = cos
(1
2x
)Amplitude
Period
Range
x-interceptsx
y
![Page 8: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/8.jpg)
48 Aratari, Trigonometry: Quiz 2.1–2.2 Form B
2. Find an equation in the form y = A sin[B(x − C)], or y = A cos[B(x − C)] that represents the graph. More thanone answer is possible.
a.
–5
–1
6
x
y
2�
2�–
b.
–3
1
x
y
2��–2� –�
![Page 9: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/9.jpg)
Aratari, Trigonometry: Chapter 2-Form A Name: 49
Take the Quiz2.1–2.4
1. Graph a minimum of one period of each of the following. Label critical points and fill in the requested information.
a. y = 5 sin(2x)Period
Amplitude
x-intercepts
x
y
b. y = 3 cos(x − π
2
)Period
Amplitude
Range
Phase Shiftx
y
![Page 10: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/10.jpg)
50 Aratari, Trigonometry: Quiz 2.1–2.4 Form A
2. Graph one period of y = tan
(1
4x
).
Period
Asymptotes
x
y
3. Find an equation that represents the circular function graph. (The guide function has been dotted in.)
�–� x
y
2
–12�
2�–
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Aratari, Trigonometry: Chapter 2-Form B Name: 51
Take the Quiz2.1–2.4
1. Graph at least one cycle of each of the following and label the critical points for one cycle. Where necessary, fill inthe blanks with the requested information.
a. y = 2 sin
(1
4x
)Period
Amplitude
x-intercepts
x
y
b. y = 4 cos(x + π
2
)Period
Amplitude
Phase Shift
x
y
![Page 12: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/12.jpg)
52 Aratari, Trigonometry: Quiz 2.1–2.4 Form B
2. Graph one period of y = cot
(1
2x
).
Period
Asymptotes
x
y
3. Find an equation that represents the circular function graph. (The dotted graph represents the guide function.)
�–� x
y
1
–1
–5
4�
![Page 13: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/13.jpg)
Aratari, Trigonometry: Chapter 2-Form A Name: 53
Take the Quiz2.5
1. Rewrite each expression to eliminate the inverse notation. Then find the exact value for y in the restricted rangewithout using a calculator.
a. y = arccos
√2
2⇒ cos =
y =
b. y = tan−1
√3
3⇒ tan =
y =
c. y = sin−1
(−
√3
2
)⇒ sin =
y =
d. y = arcsec(−2) ⇒ sec =
y =
2. Use a calculator to find an approximation to four decimal places for each expression.
a. arcsin(−0.87) b. csc−1 5
![Page 14: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/14.jpg)
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Aratari, Trigonometry: Chapter 2-Form B Name: 55
Take the Quiz2.1–2.5
1. Sketch the graph of each function for two cycles. Label x-intercepts and asymptotes (if applicable).
a. y = tan[2(x + π
4
)]
x
y
b. y = − csc1
4x
x
y
2. Find an equation of a sinusoidal function that represents the graph .
–4
4
x
y
�–2� 2�–�
![Page 16: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/16.jpg)
56 Aratari, Trigonometry: Quiz 2.1–2.5 Form B
3. Rewrite each expression to eliminate the inverse notation. Then find the exact value for y in the restricted rangewithout using a calculator. If no value for y is possible, explain why.
a. y = arccos
√3
2b. y = tan−1(−1)
c. y = sin−1
(−
√2
2
)d. y = arccsc
1
2
4. Use a calculator to find an approximation to four decimal places for each expression.
a. arcsin(0.5559) b. cot−1(
5
17
)
![Page 17: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/17.jpg)
Aratari, Trigonometry: Chapter 2 Test-Form A Name: 57
Chapter 2 Test
1–5 Without using a graphing utility, graph two cycles of the given function. Provide the requested information.
1. y = 4 cos(−2x)Period
Amplitude
Range
x
y
2. y = sin
[1
2(x + π)
]Period
Amplitude
Phase Shift
x-interceptsx
y
![Page 18: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/18.jpg)
58 Aratari, Trigonometry: Test Form A
3. y = − cot(4x)Period
x-intercepts
asymptotes
x
y
4. y = 4 csc(x − π
2
)Period
Range
x
y
5. y = cos(π
2x)
+ 2
Period
Range
x
y
![Page 19: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/19.jpg)
Aratari, Trigonometry: Chapter 2 Test-Form A Name: 59
6. Find an equation for each circular functions graph.
a. y = b. y =
–3
2
x
y
2�
2�–
–3
x
y
4�–4�
c. y = d. y =
x
y
1
2
–1
–2
2�
23�
2�– –3
3
x
y
2�
2�–
![Page 20: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/20.jpg)
60 Aratari, Trigonometry: Test Form A
7. Without the use of a calculator, find the exact value for y.
a. y = arccos 0 b. y = arctan(−1)
c. y = sin−1(
1
2
)d. y = arcsec
2√3
e. y = cot−1
(√3
3
)f. y = csc−1
(−√
2)
g. y = cos−1(
−1
2
)h. y = sin−1(−1)
i. y = sin
(arctan
(−
√3
3
))j. y = tan
(arccos
15
17
)
8–11 Use your calculator to find an approximation to four decimal places for each expression.
8. sin−1(−0.45) 9. arctan 53.2
10. csc−1(
−13
7
)11. sec(arctan 2.5)
12. Solve the equation 7 cos 4x = 2 for x. Assume the arc restrictions are those specified in the definition for thearccosine.
![Page 21: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/21.jpg)
Aratari, Trigonometry: Chapter 2 Test-Form A Name: 61
13. Identify the inverse circular function graph: y =
1–1x
y
2�
2�–
14. The graph below models the body temperature in degrees Fahrenheit for a five day illness.
1 2 3 4 5
98°
100°
104°
Day
a. On which days (to the nearest half-day) will the temperature be 101◦?
b. Approximate the number of days (to the nearest half-day) between the 101◦ temperatures.
c. Approximate the difference in the temperatures (to the nearest degree) between the highest and lowest
temperatures.
![Page 22: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/22.jpg)
![Page 23: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/23.jpg)
Aratari, Trigonometry: Chapter 2-Form B Name: 63
Chapter 2 Test
1–5 Without using a graphing utility, graph two cycles of the given function. Provide the requested information.
1. y = 3 sin
(−1
4x
)Period
Amplitude
Range
x
y
2. y = cos[2(x + π
4
)]Period
Amplitude
Phase Shift
x-interceptsx
y
![Page 24: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/24.jpg)
64 Aratari, Trigonometry: Chapter 2 Test Form B
3. y = − tan
(1
3x
)Period
x-intercepts
asymptotes
x
y
4. y = 4 sec xPeriod
Range
x
y
5. y = sin(π
3x)
− 1
Period
Range
x
y
![Page 25: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/25.jpg)
Aratari, Trigonometry: Chapter 2-Form B Name: 65
6. Find an equation for each of the following circular functions.
a. y = b. y =
1
2
x
y
3�
3�–
4
2
x
y
� 2�2�
6�
c. y = d. y =
�–2� 2� x
y
2
1
–2
�–� x
y
2
–1
![Page 26: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/26.jpg)
66 Aratari, Trigonometry: Chapter 2 Test Form B
7. Without the use of a calculator, find the exact value for y.
a. y = arcsin 1 b. y = arccot√
3
c. y = cos−1(
1
2
)d. y = arccsc
2√3
e. y = tan−1(−1) f. y = sec−1(−√
2)
g. y = sin−1(
−1
2
)h. y = cos−1(−1)
i. y = cos
(arctan
(−
√3
3
))j. y = sin
(arccos
15
17
)
8–11 Use your calculator to find an approximation to four decimal places for each expression.
8. cos−1(−0.45) 9. arctan 89
10. sec−1(
−13
7
)11. cot(arctan 2.5)
12. Solve the equation 7 sin 4x = 5 for x. Assume the arc restrictions are those specified in the definition for thearcsine.
![Page 27: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/27.jpg)
Aratari, Trigonometry: Chapter 2-Form B Name: 67
13. Identify the inverse circular function graph: y =
1–1x
y
�
14. The graph below models the body temperature in degrees Fahrenheit for a five day illness.
1 2 3 4 5
98°
100°
104°
Day
a. On which days (to the nearest day) will the temperature be 102◦?
b. Approximate the number of days (to the nearest day) between the 102◦ temperatures.
c. Approximate the difference in the temperatures (to the nearest degree) between the highest and lowest
temperatures.
![Page 28: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/28.jpg)
![Page 29: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/29.jpg)
Aratari, Trigonometry: Chapter 2-Form C Name: 69
Chapter 2 Test
1–5 Without using a graphing utility, graph two cycles of the given function. Provide the requested information.
1. y = 3 cos
(−1
4x
)Period
Amplitude
Range
x
y
2. y = sin[2(x + π
4
)]Period
Amplitude
Phase Shift
x-interceptsx
y
![Page 30: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/30.jpg)
70 Aratari, Trigonometry: Chapter 2 Test Form C
3. y = − cot
(1
3x
)Period
x-intercepts
asymptotes
x
y
4. y = 4 csc xPeriod
Range
x
y
5. y = cos(π
3x)
− 1
Period
Range
x
y
![Page 31: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/31.jpg)
Aratari, Trigonometry: Chapter 2-Form C Name: 71
6. Find an equation for each of the following circular functions.
a. y = b. y =
4
x
y
3�–3�x
y
1
–1
4�
43�
4�–
c. y = d. y =
2
1
x
y
611�
6�–
4
x
y
2��–1
![Page 32: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/32.jpg)
72 Aratari, Trigonometry: Chapter 2 Test Form C
7. Without the use of a calculator, find the exact value for y.
a. y = arccos1
2b. y = arctan 0
c. y = sin−1
(√2
2
)d. y = arccsc 2
e. y = arcsec(−1) f. y = csc−1(−√
2)
g. y = cot−1(
1√3
)h. y = sin−1(−1)
i. y = cos(arctan(−1)) j. y = sin
(arccos
8
17
)
8–11 Use your calculator to find an approximation to four decimal places for each expression.
8. sin−1 0.54 9. arccsc 89
10. cos
[tan−1
(−13
7
)]11. tan(arcsec 2.5)
12. Solve the equation 3 cos 5x = 2 for x. Assume the arc restrictions are those specified in the definition for thearccosine.
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Aratari, Trigonometry: Chapter 2-Form C Name: 73
13. Identify the inverse circular function graph: y =
x
y
2�
2�–
14. The graph below models the tides in feet, x hours after midnight for one day.
1 6 12 18 24
1
2
3
Hours
a. Approximate the times (to the nearest half-hour) for high tide.
b. Approximate the times (to the nearest half-hour) for low tide.
c. Approximate the difference in the water level (to the nearest foot) between high tide and low tide.
![Page 34: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/34.jpg)
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Aratari, Trigonometry: Chapter 2-Form D Name: 75
Chapter 2 Test
1–5 Without using a graphing utility, graph two cycles of the given function. Provide the requested information.
1. y = 4 sin(−2x)Period
Amplitude
Range
x
y
2. y = cos
[1
2(x − π)
]Period
Amplitude
Phase Shift
x-interceptsx
y
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76 Aratari, Trigonometry: Chapter 2 Test Form D
3. y = − tan(4x)Period
x-intercepts
asymptotes
x
y
4. y = 4 sec(x + π
2
)Period
Range
x
y
5. y = sin(πx) + 1Period
Range
x
y
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Aratari, Trigonometry: Chapter 2-Form D Name: 77
6. Find an equation for each of the following circular functions.
a. y = b. y =
2
x
y
–4� 4�
x
y
3�
3�–
–1
1
c. y = d. y =
3
x
y
8�
89�
87�–
x
y
2
–2 23�
2�–
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78 Aratari, Trigonometry: Chapter 2 Test Form D
7. Without the use of a calculator, find the exact value for y.
a. y = arcsin1
2b. y = arccot 0
c. y = cos−1
√2
2d. y = arcsec 2
e. y = arctan(−1) f. y = csc−1(−√
2)
g. y = cot−1(
1√3
)h. y = cos−1
(−
√3
2
)
i. y = cos(arcsin(−1)) j. y = tan
(arcsin
8
17
)
8–11 Use your calculator to find an approximation to four decimal places for each expression.
8. cos−1 0.54 9. arcsec 89
10. tan
[sin−1
(−2
5
)]11. cos(arccot 2.5)
12. Solve the equation 4 sin 3x = −2.4 for x. Assume the arc restrictions are those specified in the definition for thearcsine.
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Aratari, Trigonometry: Chapter 2-Form D Name: 79
13. Identify the inverse circular function graph: y =
1–1x
y
2�
2�–
14. The graph below models the tides in feet, x hours after midnight on a given day.
1 6 12 18 24
1
2
3
4
5
6
Hours
a. Approximate the time (to the nearest half-hour) for low tide.
b. Approximate the time (to the nearest hour) for the second high tide.
c. Approximate the difference in the water level (to the nearest foot) between high tide and low tide.
![Page 40: Take the Quiz!aplustestbank.eu/...Bank-for-Trigonometry-A-Circular-Function-Appro… · Aratari, Trigonometry: Chapter 2-Form B Name: 43 Take the Quiz 2.1 1. Graph one cycle of the](https://reader033.fdocuments.us/reader033/viewer/2022060511/5f2899c63dbea4284b00ad95/html5/thumbnails/40.jpg)
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260 Aratari, Trigonometry: Quiz 2.1 Form B
Chapter 2 Answers
Quiz 2.1 Form A
1.
x
y
2��–2� –�
2�( , 1)
23�( , –1)
1
–1
(0, 0) (2�, 0)(�, 0)
y = sin x
2.
x
y
�–2�
2�( , 0)
23�( , 0)
1
–1(�, –1)
(2�, 1)y = cos x (0, 1)
3. a. y = 7 cos x
b. y = −4 sin x
Quiz 2.1 Form B
1.
x
y
�–2�
2�( , 0)
23�( , 0)
1
–1(�, –1)
(2�, 1)y = cos x (0, 1)
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Aratari, Trigonometry: Chapter 2 Answers 261
2. Range: |y| ≤ 3
x-intercepts: x = k · π
–3
4
x
y
2�–2�
y = –3 sin x
3. a. y = 4 sin x
b. y = −2 cos x
Quiz 2.1–2.2 Form A
1. a. Amplitude: 4
Period: 2π
x-intercepts: x = π
2+ k · π
4
x
y
2��–2� –�
(0, –4)
(�, 4)
(2�, –4)
23�( , 0)
2�( , 0)
b. Amplitude: 1
Period: 8π
x-intercepts: x = k · 4π
Range: −1 ≤ y ≤ 1x
y
8�4�–8� –4�
1
–1
(0, 0) (8�, 0)
(6�, –1)
(4�, 0)
(2�, 1)
2. a–b Other answers are possible
a. y = 2 sin(x + π
4
), y = 2 cos
(x − π
4
)
b. y = −6 cos
(1
2x
), y = 6 sin
[1
2(x − π)
]
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262 Aratari, Trigonometry: Quiz 2.1–2.4 Form A
Quiz 2.1–2.2 Form B
1. a. Amplitude: 2
Period: 2π
Range: |y| ≤ 2
x-intercepts: x = k · π
–3
x
y
2��–2� –�
(�, 0) (2�, 0)
23�( , –2)
2�( , 2)
(0, 0)
y = 2 sin x
b. Amplitude: 1
Period: 4π
Range: |y| ≤ 1
x-intercepts: x = π + k · 2πx
y
4�2�–4�
–1
(0, 1)
(2�, –1)
(3�, 0)
(4�, 1)
(�, 0)
y = cos( x)12
2. a–b Other answers are possible
a. y = −5 sin 4x, y = 5 sin[4(x + π
4
)]
b. y = 3 cos(x + π
4
), y = 3 sin
(x + 3π
4
)
Quiz 2.1–2.4 Form A
1. a. Period: π
Amplitude: 5
x-intercepts: x = k · π2
5
x
y
�–�
(�, 0)(0, 0)
4�( , 5)
2�( , 0)
43�( , –5)
y = 5 sin (2x)
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Aratari, Trigonometry: Chapter 2 Answers 263
b. Period: 2π
Amplitude: 3
Range: |y| ≤ 3
Phase Shift: rightπ
2
3
–3
x
y
2��–2�
(2�, 0)(�, 0)(0, 0)
2�( , 3)
2�(x – )
23�( , –3)
y = 3 cos
2. Period: 4π
Asymptotes: x = 2π + k · 4π
x
y
2�–2�
2
1y = tan 1
4
3. y = 4 csc 2x
Quiz 2.1–2.4 Form B
1. a. Period: 8π
Amplitude: 2
x-intercepts: x = k · 4π 2
x
y
–8� 8�4�
(8�, 0)(4�, 0)
(6�, –2)
(2�, 2)
(0, 0)
y = 2 sin( x)14
b. Period: 2π
Amplitude: 4
Phase Shift: leftπ
2
4
–4
x
y
–2� 2�
(2�, 0)
(�, 0)
23�( , 4)
( , –4)
2�
2�
(x + )
(0, 0)
y = 4 cos
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264 Aratari, Trigonometry: Quiz 2.5 Form A
2. Period: 2π
Asymptotes: x = k · 2π
21
x
y
–2� 2��
y = cot( x)12
3. y = 5 sec 2x
Quiz 2.5 Form A
1. a. cos y =√
2
2
y = π
4
b. tan y =√
3
3
y = π
6
c. sin y = −√
3
2
y = −π
3
d. sec y = −2
cos y = −1
2
y = 2π
3
2. a. −1.0552
b. 0.2014
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Aratari, Trigonometry: Chapter 2 Answers 265
Quiz 2.1–2.5 Form B
1. a. x-intercepts: x = π
4+ k · π
2Asymptotes: x = k · π
2
x
y
2�
2�–
–1
y = tan �4
b. x-intercepts: none
Asymptotes: x = k · 4π
–8� 8�–1
1
x
y y = –csc x14
2. y = − cos x + 2, y = sin(x − π
2
)+ 2
3. a. cos y =√
3
2
y = π
6
b. tan y = −1
y = −π
4
c. sin y = −√
2
2
y = −π
4
d. csc y = 1
2
sin y = 2 ⇒ not possible, since sin y can not be greater than 1.
4. a. 0.5894
b. 1.2847
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266 Aratari, Trigonometry: Chapter 2 Test Form A
Chapter 2 Test Form A
1.
–4
4
x
y
�–�
y = 4 cos(–2x) Period π
Amplitude 4
Range |y| ≤ 4
2.
–1
1
x
y
4�–4�
y = sin[ (x + �)]12
Period 4π
Amplitude 1
Phase Shift left π
x-intercepts x = π + k · 2π
3.
–1
1
x
y
4�
4�–
y = –cot(4x)
Periodπ
4x-intercepts x = π
8+ k · π
4
Asymptotes x = k · π4
4.
1
x
y
2�
–2�2
3�2�
23�
2�––
(x – )y = 4 csc
Period 2π
Range |y| ≥ 4
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Aratari, Trigonometry: Chapter 2 Test Answers 267
5.
3
x
y
2 4 6 8
2�( x)y = cos + 2
Period 4
Range 1 ≤ y ≤ 3
6. a–d Other answers are possible
a. y = −2 sin 4x b. y = − cot
(1
4x
)
c. y = 2 sec x d. y = 3 cos(x − π
4
)7. a. y = π
2b. y = −π
4
c. y = π
6d. y = π
6
e. y = π
3f. y = −π
4
g. y = 2π
3h. y = −π
2
i. y = −1
2j. y = 8
15
8. −0.4668 9. 1.5520
10. −0.5686 11. 2.6926
12. x = 1
4cos−1
(2
7
)≈ 0.3203
13. y = arcsin x
14. a. 1 day, 31
2days
b. 21
2days
c. 6◦
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268 Aratari, Trigonometry: Chapter 2 Test Form B
Chapter 2 Test Form B
1.
–1
3
x
y
8�–8�
y = 3 sin 14
Period 8π
Amplitude 3
Range |y| ≤ 3
2.
�–� x
y
–1
y = cos[2(x + )]�4
Period π
Amplitude 1
Phase Shift leftπ
4x-intercepts x = k · π
2
3.
x
y
–3
–1
1
29�
23�
23�–
y = –tan( x)13
Period 3π
x-intercepts x = k · 3π
Asymptotes x = 3π
2+ k · 3π
4.
x
y
2�–2�2�–
y = 4 sec x
–3
1
4
–4
Period 2π
Range |y| ≥ 4
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Aratari, Trigonometry: Chapter 2 Answers 269
5.
1
–3
x
y
3�
y = sin – 1
3 12
Period 6
Range −2 ≤ y ≤ 0
6. a–d Other answers are possible
a. y = cot 3x b. y = 4 sin(x − π
6
)
c. y = −2 csc
(1
2x
)d. y = sec x + 3
7. a. y = π
2b. y = π
6
c. y = π
3d. y = π
3
e. y = −π
4f. y = 3π
4
g. y = −π
6h. y = π
i. y =√
3
2j. y = 8
17
8. 2.0376 9. 1.5596
10. 2.1394 11. 0.4000
12. x = 1
4sin−1
(5
7
)≈ 0.1989
13. y = arccos x
14. a. 1 day, 3 days
b. 2 days
c. 6◦
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270 Aratari, Trigonometry: Chapter 2 Test Form C
Chapter 2 Test Form C
1.
–1x
y
–8� 8�4�
y = 3 cos(– x)14
Period 8π
Amplitude 3
Range |y| ≤ 3
2.
x
y
–� �
y = sin[2(x + )]�4
Period π
Amplitude 1
Phase Shift leftπ
4
x-intercepts x = π
4+ k · π
2
3.
x
y
3�–3�
y = –cot ( x)13
Period 3π
x-intercepts x = 3π
2+ k · 3π
Asymptotes x = k · 3π
4.
�–2� 2� x
y
4
2
y = 4 csc x
Period 2π
Range |y| ≥ 4
5.1
–1x
y
6 12
3�( x)y = cos – 1
Period 6
Range −2 ≤ y ≤ 0
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Aratari, Trigonometry: Chapter 2 Answers 271
6. a–d Other answers are possible
a. y = −4 sin
(1
3x
)b. y = 1
2sec(2x)
c. y = tan
[1
2
(x − 5π
6
)]d. y = sin x + 2
7. a. y = π
3b. y = 0
c. y = π
4d. y = π
6
e. y = π f. y = −π
4
g. y = π
3h. y = −π
2
i. y =√
2
2j. y = 15
17
8. 0.5704 9. 0.0112
10. 0.4741 11. 2.2913
12. x = 1
5cos−1
(2
3
)≈ 0.1682
13. y = arctan x
14. Answers can be slightly off due to the quality of the graph.
14. a. 2:30 am, 3 pm
b. 8:30 am, 9:30 pm
c. 1 ft
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272 Aratari, Trigonometry: Chapter 2 Test Form D
Chapter 2 Test Form D
1.
–4
x
y
�–�
y = 4 sin (–2x)Period π
Amplitude 4
Range |y| ≤ 4
2.
x
y
4��–4�
1
–1
y = cos[ (x – �)]12
Period 4π
Amplitude 1
Phase Shift right π
x-intercepts x = k · 2π
3.
x
y
–3
–1
1
83�
8�–
8�
y = –tan (4x)
Periodπ
4x-intercepts x = k · π
4
Asymptotes x = π
8+ k · π
4
4.
x
y
2�–2� –�
y = 4 sec
2
–2
(x + )�2
Period 2π
Range |y| ≥ 4
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Aratari, Trigonometry: Chapter 2 Answers 273
5.
1
–1x
y
1 2 4
y = sin(�x) + 1
Period 2
Range 0 ≤ y ≤ 2
6. a–d Other answers are possible
a. y = −2 cos
(1
2x
)b. y = − cot(3x)
c. y = 3 sin(x − π
8
)d. y = 2 sec x − 2
7. a. y = π
6b. y = π
2
c. y = π
4d. y = π
3
e. y = −π
4f. y = −π
4
g. y = π
3h. y = 5π
6
i. y = 0 j. y = 8
15
8. 1.0004 9. 1.5596
10. −0.4364 11. 0.9285
12. x = 1
3arcsin
(−2.4
4
)≈ −0.2145
13. y = arcsin x
14. Answers can be slightly off due to the quality of the graph.
14. a. 10:30 am
b. 6 pm
c. 4 ft