AnswersAZ-Common Core Algebra II BGraphing Tangent and Cotangent

Graphing Tangent and Cotangent — Unit test Answers

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1
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Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

Question illustration
A
step 1;
Option A
B
step 1;
Option B
C
step 4; cos(x)
D
step 4; csc(x)
2
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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
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

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
5

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
6

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
7

Judy knows that the function graphed below is a transformation of the parent function . Since the period and asymptotes are the same as those of the parent function, she knows that there were no horizontal stretches, compressions, or translations. She can also tell that there were no reflections since the general shape of the graph is the same as that of the parent function. Which statement is correct regarding the transformations that were applied?

Question illustration
A
Since the y-intercept of the graph is , the graph of the parent function was translated 0.5 units down, and since the graph passes through the point instead of , the graph was vertically compressed.
Option A
B
Since the y-intercept of the graph is , the graph of the parent function was translated 0.5 units down, and since the graph passes through the point instead of , the graph was vertically stretched.
Option B
C
Since the y-intercept of the graph is , the graph of the parent function was translated 1.5 units down, and since the graph passes through the point instead of , the graph was vertically compressed.
Option C
D
Since the y-intercept of the graph is , the graph of the parent function was translated 1.5 units down, and since the graph passes through the point instead of , the graph was vertically stretched.
Option D
8

Which statement accurately describes how adding a number, n, to the function affects its graph?

Question illustration
A
There is a vertical shift of n units.
B
The x-intercepts will shift n units.
C
There is a change in amplitude of n units.
D
The range will change by a factor of 2n units.
9

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
10

Which of the following is cot() sec() in simplified form?

Question illustration
A
csc
Option A
B
tan
Option B
C
–1
D
1
11

What is the amplitude of the cosine function corresponding to the secant function graphed below?

Question illustration
A
–2
B
–1
C
2
D
3
12

Which is the graph of the function ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The curve crosses the x axis at (pi comma 0), (0 comma 0) and (negative pi comma 0).
Option A
B
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The curve crosses the x axis at (pi comma 0), (0 comma 0) and (negative pi comma 0).
Option B
C
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 4. The curve crosses the x axis at (pi by 2 comma 0) and (negative 3 pi by 4 comma 0). The y-intercept is at (0 comma negative 2).
Option C
D
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 4. The curve crosses the x axis at (pi by 2 comma 0) and (negative 3 pi by 4 comma 0). The y-intercept is at (0 comma negative 1).
Option D
13

A student uses the equation to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline , where . To solve the problem, the student used the given value of to find the value of and then substituted the value of in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?

Question illustration
A
5.3
B
7.5
C
9.2
D
28.3
14

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
15

An angle that shares the same sine value of an angle that measures radians is located where?

Question illustration
A
Quadrant I
B
Quadrant II
C
Quadrant IV
D
along an axis
16

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
17

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
18

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
19

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
20

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

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