AnswersAlgebra 2 MP 234 CHSGraphing Sine and Cosine

Graphing Sine and Cosine — Unit test Answers

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1
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The graph of which function passes through (0,3) and has an amplitude of 3?

A
f (x) = sine (x) + 3
Option A
B
f (x) = cosine (x) + 3
Option B
C
f (x) = 3 sine (x)
Option C
D
f (x) = 3 cosine (x)
Option D
2
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Which statement accurately describes how adding a number, n, to the function affects its graph?

Question illustration
A
There is a vertical shift of n units.
B
The x-intercepts will shift n units.
C
There is a change in amplitude of n units.
D
The range will change by a factor of 2n units.
3

An angle measuring (870n)° is in standard position. For which value of n will the terminal side fall on the y-axis?

A
n = 3
B
n = 4
C
n = 5
D
n = 6
4

Which transformations are needed to change the parent sine function to the sine function below?

Question illustration
A
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left
Option A
B
vertical stretch of 2, horizontal compression to a period of , vertical shift of 2 units up, phase shift of units left
Option B
C
vertical stretch of , horizontal compression to a period of , vertical shift of 1 unit up, phase shift of units left
Option C
D
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit down, phase shift of units left
Option D
5

Which measure is of an angle that is coterminal with a 95° angle?

A
95° – (1,450n)°, for any integer n
B
95° – (1,080n)°, for any integer n
C
95° – (780n)°, for any integer n
D
95° – (340n)°, for any integer n
6

A student is given that point P(a, b) lies on the terminal ray of angle , which is between radians and 2 radians. The student uses the steps below to find cos . Step 1Find the quadrant in which P(a, b) lies:P(a, b) is in Quadrant IV.Step 2Use the point and the Pythagorean theorem to determine the value of r:, but since r must be positive, .Step 3Determine cos ., where a and b are positive.Which of the following explains whether the student is correct?

Question illustration
A
The student made an error in step 3 because a is positive in Quadrant IV; therefore, .
Option A
B
The student made an error in step 3 because .
Option B
C
The student made an error in step 2 because r is negative in Quadrant IV; therefore, .
Option C
D
The student made an error in step 2 because using the Pythagorean theorem gives .
Option D
7

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

Question illustration
A
The reference angle should be , and the sign of the value should be negative.
Option A
B
The reference angle should be , and the cosine value for is .
Option B
C
The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting in the first step.
Option C
D
The cosine value for is , and the reference angle and quadrant should be determined by subtracting in the first step.
Option D
8

How is the graph of transformed to produce the graph of ?

Question illustration
T
The graph is stretched horizontally by a factor of 2 and then moved right 4 units.
T
The graph is compressed horizontally by a factor of 2 and then moved down 4 units.
T
The graph is compressed horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
T
The graph is stretched horizontally by a factor of 2, moved left 4 units, and moved down 4 units.
9

Which of the following represents the measures of all angles coterminal with a –220° angle?

A
360 + 140n, for any whole number n
B
360 + 140n, for any integer n
C
140+ 360n, for any whole number n
D
140 + 360n, for any integer n
10

If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec ?

Question illustration
A
Negative five-thirds
Option A
B
Negative five-fourths
Option B
C
Five-fourths
Option C
D
Five-thirds
Option D
11

What is the general equation of a sine function with an amplitude of 6, a period of , and a horizontal shift of ?

Question illustration
A
y = sine (8 (x minus StartFraction pi Over 2 EndFraction))
Option A
B
y = 8 sine (4 (x minus StartFraction pi Over 2 EndFraction))
Option B
C
y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))
Option C
D
y = 6 sine (8 x) + StartFraction pi Over 2 EndFraction
Option D
12

What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

Question illustration
A
5.8 ft
B
6.3 ft
C
27.5 ft
D
69.1 ft
13

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option D
15

How long is the arc intersected by a central angle of radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3.14 for .

Question illustration
A
1.0 ft
B
5.7 ft
C
6.3 ft
D
7.0 ft

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