AnswersPrecalculusSolving Trigonometric Equations

Solving Trigonometric Equations — Cumulative exam Answers

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1
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What is the length of side m in shown below, given M = 35° and P = 65° and p = 20? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
10.4
B
12.7
C
31.6
D
38.5
2
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Ingrid claims that . Review Ingrid’s steps in verifying her claim.Which statement describes Ingrid’s claim that and her steps in verifying her claim?

Question illustration
A
Ingrid’s claim is correct, and her steps are correct.
B
Ingrid’s claim is correct, but her steps are incorrect.
C
Ingrid’s claim is incorrect, but her steps are correct.
D
Ingrid’s claim is incorrect, and her steps are incorrect.
3

To produce the graph of the function , what transformations should be applied to the graph of the parent function ?

Question illustration
A
a horizontal compression to produce a period of and a vertical compression
Option A
B
a horizontal compression to produce a period of and a vertical stretch
Option B
C
a horizontal stretch to produce a period of and a vertical compression
Option C
D
a horizontal stretch to produce a period of and a vertical stretch
Option D
4

What is the exact value of cos(c + d), given for c in Quadrant II and for d in Quadrant III?

Question illustration
A
Negative StartFraction 47 Over 100 EndFraction
Option A
B
Negative 1 and StartFraction 3 Over 100 EndFraction
Option B
C
StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction
Option C
D
StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction
Option D
5

Which trigonometric functions have a domain of [–1, 1]?

A
y = arcsinx and y = arccosx
B
y = arccosx and y = arctanx
C
y = arcsinx and y = arctanx
D
y = arcsecx and y = arccscx
6

Suppose and sin(x) > 0. What is the value of tan(2x)?

Question illustration
A
Negative 5
Option A
B
Negative four-thirds
Option B
C
Four-thirds
Option C
D
2
7

What is the value of x in ?

Question illustration
A
Negative StartFraction 2 pi Over 3 EndFraction
Option A
B
Negative StartFraction pi Over 6 EndFraction
Option B
C
StartFraction 2 pi Over 3 EndFraction
Option C
D
StartFraction 7 pi Over 6 EndFraction
Option D
8

Given: < A < and , < B < What is the value of cos(A – B)?

Question illustration
A
Negative StartFraction 2 StartRoot 5 EndRoot Over 25 EndFraction
Option A
B
Negative StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
StartFraction 11 StartRoot 5 EndRoot Over 25 EndFraction
Option D
9

Which expression is equivalent to 3cos2?

Question illustration
A
(cos(ϴ) – 1)
Option A
B
(cos(ϴ) – 5)
Option B
C
3(cos(ϴ) + 2)
D
3(cos(ϴ) + 1)
10

What are all the exact solutions of for ? Give your answer in radians.

Question illustration
A
mc017-3.jpg
Option A
B
and
Option B
C
and
Option C
D
, and
Option D
11

Sheila is building a triangular sandbox in her backyard. She has obtained the measurements in the diagram below. The angle is measured in degrees. [Not drawn to scale]What is the unknown side length (x)? Round the answer to the nearest tenth.

Question illustration
A
5.6 ft
B
6.4 ft
C
31.5 ft
D
40.5 ft
12

Which is equivalent to cos-1(0)? Give your answer in radians.

A
0
B
mc005-1.jpg
Option B
C
mc005-2.jpg
Option C
D
mc005-3.jpg
Option D
13

What is 4cos2(165°) – 2 expressed as a single trigonometric function?

A
4cos(330°)
B
2cos(330°)
C
4cos(82.5°)
D
2cos(82.5°)
14

Which is an x-intercept of the graph of the function ?

Question illustration
A
(StartFraction pi over 6 EndFraction, 0)
Option A
B
(StartFraction pi over 3 EndFraction , 0)
Option B
C
(3pi, 0)
Option C
D
(6pi, 0)
Option D
15

Which of the following is the graph of the function y = 4csc(x)?

A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3) and y equals negative 5 at (3 pi by 2 comma negative 5) and (negative pi by 2 comma negative 5).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 5 at (pi by 2 comma 5) and (negative 3 pi by 2 comma 5) and y equals negative 3 at (3 pi by 2 comma 3) and (negative pi by 2 comma 3).
Option B
C
On a coordinate plane, the x axis ranges from negative pi to 3 pi with an interval of pi units and the y axis ranges from negative 8 to 8 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 4 at (5 pi by 2 comma 4) and (pi by 2 comma 4) and y equals negative 4 at (3 pi by 2 comma negative 4) and (negative pi by 2 comma negative 4).
Option C
D
On a coordinate plane, the x axis ranges from negative pi to 3 pi with an interval of pi units and the y axis ranges from negative 8 to 8 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 4 at (9 pi by 5 comma 4) and (pi by 5 comma 4) and y equals negative 4 at (14 pi by 5 comma negative 4) and (negative 4 pi by 5 comma negative 4).
Option D
16

Which expression is equivalent to ?

Question illustration
A
StartFraction negative 1 minus tangent (2 x) Over 1 minus (negative 1) (tangent (2 x) ) EndFraction
Option A
B
StartFraction negative 1 minus tangent (2 x) Over 1 + (negative 1) (tangent (2 x) ) EndFraction
Option B
C
StartFraction 1 minus tangent (2 x) Over 1 + (1) (tangent (2 x) ) EndFraction
Option C
D
StartFraction 1 + tangent (2 x) Over 1 minus (1) (tangent (2 x) ) EndFraction
Option D
17

What is the vertical shift of the graph of the parent cosecant function to the graph of the function below?

Question illustration
A
1 unit down
B
2 units down
C
3 units down
D
4 units down
18

What is the exact value of ?

Question illustration
A
Negative StartFraction StartRoot 2 minus StartRoot 2 EndRoot EndRoot Over 4 EndFraction
Option A
B
Negative StartFraction StartRoot 2 + StartRoot 2 EndRoot EndRoot Over 4 EndFraction
Option B
C
Negative StartFraction StartRoot 2 minus StartRoot 2 EndRoot EndRoot Over 2 EndFraction
Option C
D
Negative StartFraction StartRoot 2 + StartRoot 2 EndRoot EndRoot Over 2 EndFraction
Option D
19

What are the x-intercepts of the graph of the function ? Use your graphing calculator to estimate the answer.

Question illustration
A
, where n is any integer
Option A
B
, where n is any integer
Option B
C
, where n is any integer
Option C
D
, where n is any integer
Option D
20

Which equation represents the Law of Sines for ?

Question illustration
A
StartFraction sine A over b EndFraction = StartFraction sine B over a EndFraction
Option A
B
c Sine C = b sine B
Option B
C
StartFraction sine A over a EndFraction = StartFraction sine B over b EndFraction
Option C
D
b Sine B = a sine A
Option D

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