Answers AL-Algebra II with StatisticsUnit Test

Unit Test — Unit test Answers

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If , which of the following represents approximate values of and , for ?

sine theta almost-equals 0.9511; tangent theta almost equals 0.3249

sine theta almost-equals 0.9511; tangent theta almost equals 3.0780

sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955

sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731

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Which is equivalent to ? Give your answer in radians.

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Which of the following could be the equation of the function below?

y = negative 3 sine (2 (x + pi)) + 2

y = negative 3 sine (x + pi) + 2

y = 3 sine (4 (x minus pi)) + 4

y = 3 sine (2 (x + pi)) + 2

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.

0 seconds

1.38 seconds

4.62 seconds

8 seconds

Which is the graph of y = cos(x) + 3?

On a coordinate plane, a cosine curve has a maximum of 3 and a minimum of negative 3.

On a coordinate plane, a cosine curve has a maximum of 4 and a minimum of negative 2.

On a coordinate plane, a cosine curve has a maximum of negative 2 and a minimum of negative 4.

On a coordinate plane, a cosine curve has a maximum of 6 and a minimum of negative 0.

Which function describes the graph below?

f (x) = 6 cosine (x)

f (x) = 3 cosine (x) + 3

f (x) = 6 sine (x)

f (x) = 3 sine (x) + 3

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

P(, –2)

P (, –2)

P(–2, )

Which of the following is true of the location of an angle, , whose tangent value is ?

has a 30-degree reference angle and is located in Quadrant II or IV

has a 30-degree reference angle and is located in Quadrant II or III

has a 60-degree reference angle and is located in Quadrant II or IV

has a 60-degree reference angle and is located in Quadrant II or III

The angle measures associated with which set of ordered pairs share the same reference angle?

(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)

(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Which of the following is the graph of y = cos(2x)?

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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 . Which of the following is the graph of this equation?

On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).

On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).

On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).

On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).

What is the simplest form of the expression below?

sec

cot

csc

tan

Haruto simplified the value below.Which statement explains whether Haruto is correct?

Haruto is correct because the angle is coterminal with and the reference angle is .

Haruto is correct because the angle is coterminal with , which is also the reference angle.

Haruto is not correct because the angle is coterminal with , and .

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35

h = negative 10 sine (Pi t) + 35

h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35

h = 10 sine (Pi t) + 35

What is the range of y = –3sin(x) – 4?

all real numbers

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

(–5, 12)

(5, –12)

(–12, 5)

(12, –5)

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5