AnswersAlgebra 2 MP 234 CHSChanges in Period and Phase Shift of Sine and Cosine Functions

Changes in Period and Phase Shift of Sine and Cosine Functions — Unit test Answers

15 verified answers
1
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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
2
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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
3

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?

Question illustration
A
One-fifth
Option A
B
StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
2
Option D
4

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
5

Which function is the same as ?

Question illustration
A
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option A
B
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option B
C
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option C
D
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Option D
6

A circle has a central angle measuring radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for .

Question illustration
A
3.7 cm
B
4.9 cm
C
14.3 cm
D
15.4 cm
7

Which of the following are in correct order from greatest to least?

A
, 330°, , ,
Option A
B
, , , , 330°
Option B
C
, , , , 330°
Option C
D
330°, , , ,
Option D
8

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
9

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
10

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
11

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
12

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
13

Which of the following is true for f(x) = –2sin(x) – 3?

A
The range of the function is the set of real numbers .
Option A
B
The graph of the function is the graph of f(x) = –2sin(x) shifted 3 units up.
C
The amplitude of the function is 2.
D
The period of the function is .
Option D
14

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
15

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

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