Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Transformations of Functions

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Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

155°

160°

165°

170°

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Which of the following represents the measures of all angles coterminal with a 418° angle?

360 + 58n, for any whole number n

58 + 360n, for any integer n

58 + 360n, for any whole number n

360 + 58n, for any integer n

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

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

y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2

y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2

y = 0.5 cosine (4 (x + pi)) + 2

y = 0.5 cosine (2 (x minus pi)) minus 2

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.

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)

What is 270° converted to radians?

StartFraction pi Over 6 EndFraction

StartFraction 3 Over 2 EndFraction

StartFraction 3 pi Over 2 EndFraction

If , which equation represents ?

cotangent theta = StartFraction StartRoot 15 EndRoot Over 8 EndFraction

cotangent theta = StartFraction StartRoot 15 EndRoot Over 7 EndFraction

cotangent theta = StartFraction 7 StartRoot 15 EndRoot Over 15 EndFraction

cotangent theta = StartFraction 8 StartRoot 15 EndRoot Over 15 EndFraction

What is the exact value of ?

–1

Negative StartRoot 2 EndRoot

StartRoot 2 EndRoot

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

all real numbers

An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall on the x-axis?

n = 4

n = 5

n = 6

n = 7

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

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.

The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.

The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.

The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.

What is the length of x in the diagram below?

StartFraction 5 Over StartRoot 3 EndRoot

StartFraction 10 Over StartRoot 3 EndRoot EndFraction

5 StartRoot 3 EndRoot

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

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).

Which of the following best explains the value of on the unit circle below?

The length opposite the angle is the vertical distance from the x-axis on the graph.

The length adjacent to the angle is the vertical distance from the x-axis on the graph.

The length opposite the angle is the horizontal distance from the y-axis on the graph.

The length adjacent to the angle is the horizontal distance from the y-axis on the graph.

If angle B measures 25°, what is the approximate perimeter of the triangle below?

10.3 units

11.8 units

22.1 units

25.2 units

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)

Based on the family the graph below belongs to, which equation could represent the graph?

y = StartFraction 1 Over x + 2 EndFraction + 3

y = 0.2 Superscript x Baseline + 3

y = x cubed + 3

y = log x + 3

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

y = x cubed minus 4

y = (x minus 4) cubed

y = (negative x minus 4) cubed

y = (negative x) cubed minus 4

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

What are the values of m and in the diagram below?

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.

The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.

The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.

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

The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.

The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.

The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.

An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall on the x-axis?

n = 4

n = 5

n = 6

n = 7

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

14.1 in.

22.5 in.

42.3 in.

56.5 in.

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

all real numbers

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

reciprocal

square root

exponential

quadratic

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

y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2

y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2

y = 0.5 cosine (4 (x + pi)) + 2

y = 0.5 cosine (2 (x minus pi)) minus 2

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

h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5

h = cosine (StartFraction pi Over 12 EndFraction t) + 9

h = cosine (StartFraction pi Over 6 EndFraction t) + 9

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

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

mc008-1.jpg

mc008-2.jpg

mc008-3.jpg

mc008-4.jpg

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

0.4 radian

1.0 radian

2.7 radians

5.0 radians

Which function will have a y-intercept at –1 and an amplitude of 2?

f (x) = negative sine (X) minus 1