AnswersOH-Algebra II CRUnit Test

Unit Test — Unit test Answers

15 verified answers
1
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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
2
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?

Question illustration
A
a feet
B
b feet
C
h feet
D
k feet
3

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is , what are the values of a and k?

Question illustration
A
a = –60; k = 20
B
a = –50; k = 30
C
a = –30; k = 50
D
a = –20; k = 60
4

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
5

Which values for have the same reference angles?

Question illustration
A
, ,
Option A
B
, ,
Option B
C
, ,
Option C
D
, ,
Option D
6

An angle in standard position measures radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle?

Question illustration
A
–1
B
0
C
1
D
undefined
7

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
8

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

A
d = negative 3.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 5
Option A
B
d = negative 3.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 5
Option B
C
d = negative 2.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 6
Option C
D
d = negative 2.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 6
Option D
9

What is the length of the hypotenuse in the triangle below?

Question illustration
A
14 cm
B
cm
Option B
C
cm
Option C
D
28 cm
10

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation , where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. Which equation also models this situation?

Question illustration
A
t = negative 35 sine (StartFraction pi Over 6 EndFraction m) + 55
Option A
B
t = negative 35 sine (StartFraction pi Over 6 EndFraction (m + 3)) + 55
Option B
C
t = 35 sine (StartFraction pi Over 6 EndFraction m) + 55
Option C
D
t = 35 sine (StartFraction pi Over 6 EndFraction (m + 3)) + 55
Option D
11

In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?

Question illustration
A
9 StartRoot 3 EndRoot
Option A
B
StartFraction 9 Over StartRoot 3 EndRoot EndFraction
Option B
C
9
D
StartFraction StartRoot 3 EndRoot Over 9 EndFraction
Option D
12

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
13

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
14

What are the exact values of the six trigonometric functions for radians?

Question illustration
A
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; secant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option A
B
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot
Option B
C
sine (Negative StartFraction 7 pi Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot
Option C
D
sine (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option D
15

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

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