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

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What is one possible solution for the triangle below?

Question illustration
A
Y Z similar to 43 point 0, m angle X similar to 94 point 6 degree, m angle Z similar to 17 point 4 degree.
Option A
B
Y Z similar to 19 point 3, m angle X similar to 85 point 4 degree, m angle Z similar to 26 point 6 degree.
Option B
C
Y Z similar to 12 point 9, m angle X similar to 17 point 4 degree, m angle Z similar to 94 point 6 degree.
Option C
D
Y Z similar to 95 point 4, m angle X similar to 26 point 7 degree, m angle Z similar to 85 point 4 degree.
Option D
2
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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
3

Solve the Law of Cosine: for cos C.

Question illustration
A
cosine C = StartFraction square of a + square of b minus square of c over 2ab EndFraction
Option A
B
cosine C = StartFraction square of a + square of b + square of c over negative 2ab EndFraction
Option B
C
cosine C = StartFraction square of c minus square of a minus square of b over 2ab EndFraction
Option C
D
cosine C = StartFraction square of negative c + square of a + square of b over negative 2ab EndFraction
Option D
4

Which pair of equations below is a result of constructing the altitude, h, in ?

Question illustration
A
sine A = StartFraction h over c EndFraction sine C = StartFraction h over a EndFraction
Option A
B
sine A = StartFraction h over c EndFraction sine B = StartFraction b over c EndFraction
Option B
C
sine A = StartFraction b over c EndFraction sine C = StartFraction b over a EndFraction
Option C
D
sine C = StartFraction h over a EndFraction sine B = StartFraction b over a EndFraction
Option D
5

Which equation could be used to solve for the measure of side q in shown below, given s = 15, S = 45°, and Q = 105°? [Not drawn to scale]

Question illustration
A
StartFraction sine 105 degree over 15 EndFraction = StartFraction sine 30 degree over q EndFraction
Option A
B
StartFraction sine 105 degree over q EndFraction = StartFraction sine 30 degree over 15 EndFraction
Option B
C
StartFraction 15 over sine 105 degree EndFraction = StartFraction q over sine 45 degree EndFraction
Option C
D
StartFraction q over sine 105 degree EndFraction = StartFraction 15 over sine 45 degree EndFraction
Option D
6

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
7

When deriving the Law of Cosines, the equation is created using the Pythagorean theorem. Use substitution to replace in the equation below and then simplify.

Question illustration
A
square of c = square of a + square of b minus 2bx
Option A
B
square of c = square of a minus square of b minus 2bx
Option B
C
square of c = square of a minus square of x + square of b minus 2bx + square of x
Option C
D
square of c = square of h + square of a + square of b minus 2bx
Option D
8

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of the largest angle in the triangle?

A
52.8°
B
60.0°
C
63.6°
D
82.9°
9

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

Question illustration
A
1.4 m
B
5.9 m
C
6.4 m
D
7.7 m
10

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
11

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
12

A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

Question illustration
A
82.3°
B
88.1°
C
93.8°
D
128.0°
13

Which formula gives the zeros of y = sin(x)?

A
for any positive integer k
Option A
B
for any integer k
Option B
C
for any positive integer k
Option C
D
for any integer k
Option D
14

From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?

Question illustration
A
119.0 ft.
B
141.8 ft.
C
185.1 ft.
D
220.6 ft.
15

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

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