AnswersS1S-OC Pre-Calculus A E3700 - AGInverse Trigonometric Functions

Inverse Trigonometric Functions — Unit test Answers

15 verified answers
1
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Review the graph of y = sin(x).

Question illustration
A
domain: [0, 2π]; range: [–1, 1]
B
domain: [–1, 1]; range: [0, 2π]
C
domain: [–1, 1]; range: (–ꝏ, ꝏ)
D
domain: (–ꝏ, ꝏ); range: [–1, 1]
2
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A circular crop field has an irrigation system in which a pipe, with one end attached to a tower at the center of the field, turns continuously to deliver water. The horizontal distance, in meters, from the tip of the pipe to the farmhouse is represented by y = , where x represents time in hours.

Question illustration
A
the length of the pipe
B
the distance between the tower and the farmhouse
C
the time it takes for the pipe to complete one full circle
D
the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse
3

Which graph represents the function y = cos(4x)?

A
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 1).
Option A
B
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 1).
Option B
C
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 0).
Option C
D
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 0).
Option D
4

What is the value of cos(tan-1(0))?

A
–1
B
0
C
1
D
StartFraction pi Over 2 EndFraction
Option D
5

The average high temperature during the hottest month in Beijing, China, is 72°F. The average high temperature during the coldest month in Beijing is 18°F. The function , where m represents the number of months after January, models the temperature throughout the year in Beijing.During which month in the year would the temperature reach 55°F?

Question illustration
A
August
B
September
C
November
D
December
6

On interval 0 ≤ x < 2π, where are the x-intercepts of y = cos(2x)?

A
StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction
Option A
B
0, π, and 2π
C
StartFraction pi Over 2 EndFraction, pi and StartFraction 3 pi Over 2 EndFraction
Option C
D
Option
Option D
7

A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
8

Which of the following is the equation of the function below?

Question illustration
A
y equal to 2 secant (x plus StartFraction pi over 6 EndFraction) plus 2.
Option A
B
y equal to 2 secant left-square-bracket 2 (x plus StartFraction pi over 6 EndFraction) plus 2.
Option B
C
y equal to 2 secant left-square-bracket 2 (x minus 2) plus StartFraction pi over 6 EndFraction.
Option C
D
y equal to 2 secant (x plus 2) plus StartFraction pi over 6 EndFraction.
Option D
9

Let cot(x) = , with 0 < x < 90°. What is sin(x)?

Question illustration
A
StartFraction 5 Over StartRoot 89 EndRoot EndFraction
Option A
B
StartFraction 8 Over StartRoot 89 EndRoot EndFraction
Option B
C
StartFraction StartRoot 89 EndRoot Over 8 EndFraction
Option C
D
StartFraction StartRoot 89 EndRoot Over 5 EndFraction
Option D
10

What restriction should be applied to y = tanx for y = arctanx to be defined?

A
Restrict the range to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option A
B
Restrict the range to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option B
C
Restrict the domain to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option C
D
Restrict the domain to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option D
11

The time it takes a spinner to stop completely is 12 seconds. If the spinner completes 6 revolutions in this time, what was the average angular velocity of the spinner, in radians per second, for the 12-second interval?

A
π
B
2π
C
4π
D
12π
12

Which is equal to –214°?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
13

Review the graph.

Question illustration
A
On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 3, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 1.
Option A
B
On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 2, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 4.
Option B
C
On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 4, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 2.
Option C
D
On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 3, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 1.
Option D
14

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground.Which equation models the height in inches of the sticker after x minutes?

A
y = 0.5 sine (180 pi x) + 13
Option A
B
y = 12.5 sine (180 pi x) + 13
Option B
C
y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13
Option C
D
y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13
Option D
15

On which interval are both the sine and cosine functions increasing?

A
(StartFraction 3 pi Over 2 EndFraction, 2 pi)
Option A
B
(StartFraction pi Over 2 EndFraction, pi)
Option B
C
(0, pi)
Option C
D
(pi, StartFraction 3 pi Over 2 EndFraction
Option D

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