AnswersIC Pre-Cal - DeeringInverse Trigonometric Functions

Inverse Trigonometric Functions Answers

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1
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Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
2
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What is the domain of y = cos-1x?

A
[–1, 1]
B
[0, π]
C
Left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option C
D
(–∞, ∞)
3

Which graph represents y = tan-1x?

A
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 A
B
On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction.
Option B
C
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 C
D
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 D
4

The average daily high temperature in Madrid peaks at 92°F in the summer and drops as low as 33°F in the winter. The temperature can be modeled by , where d represents the day number of the year (January 1 is 1, January 2 is 2, and so on). During which day is the high temperature expected to be closest to 75°F?

Question illustration
A
106
B
63
C
270
D
204
5

The water level in a harbor is described by the function , where y represents the water level measured in feet, and x represents the number of hours since high tide. The period of time between high tides is 12 hours. After approximately how many hours is the water expected to reach a depth of 28 feet the second time? Round to the nearest hour.

Question illustration
A
1 hour
B
2 hours
C
10 hours
D
12 hours
6

What is the range of y = sin-1x?

A
[–1, 1]
B
[0, π]
C
Left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option C
D
(–∞, ∞)
7

What is the value of ?

Question illustration
A
StartFraction 2 pi Over 3 EndFraction
Option A
B
StartFraction negative 2 pi Over 3 EndFraction
Option B
C
StartFraction negative pi Over 6 EndFraction
Option C
D
StartFraction pi Over 6 EndFraction
Option D
8

For what value of θ is ?

Question illustration
A
StartFraction pi Over 6 EndFraction
Option A
B
StartFraction pi Over 4 EndFraction
Option B
C
StartFraction pi Over 3 EndFraction
Option C
D
StartFraction pi Over 2 EndFraction
Option D
9

Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
10

Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = sin-1x
D
y = cos-1x
11

What function is graphed below?

Question illustration
A
y equal to cotangent (x minus StartFraction pi over 4 EndFraction)
Option A
B
y equal to tangent (x minus StartFraction pi over 4 EndFraction)
Option B
C
y equal to cotangent (x plus StartFraction pi over 4 EndFraction)
Option C
D
y equal to tangent (x plus StartFraction pi over 4 EndFraction)
Option D
12

Which function is equivalent to ?

Question illustration
A
y equal to minus tangent (x)
B
y equal to minus tangent ( x plusStartFraction pi over2 EndFraction)
C
y equal to tangent (x)
D
y equal to tangent ( x plusStartFraction pi over2 EndFraction)
13

What transformations were applied to the graph of the parent function to produce the function graphed below?

Question illustration
A
a horizontal compression to produce a period of and a horizontal translation of units to the left
Option A
B
a horizontal compression to produce a period of and a horizontal translation of units to the right
Option B
C
a horizontal stretch to produce a period of and a horizontal translation of units to the left
Option C
D
a horizontal stretch to produce a period of and a horizontal translation of units to the right
Option D
14

Which is the graph of the function ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 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. The graph increases in every pi interval as x increases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 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. The graph decreases in every pi interval as x decreases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
Option B
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 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 graph decreases in every pi interval as x decreases.The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
Option C
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 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 graph increases in every pi interval as x increases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
Option D
15

Suppose the graph of the parent function is vertically compressed to produce the graph of the function , but there are no reflections. Which describes the value of a?

Question illustration
A
a is less than minus 1
B
a is greater than minus 1 but less than 0
C
a is greater than 0 but less than 1
D
a is greater than 1
16

What is the period of the function ?

Question illustration
A
3 units
B
4 units
C
6 units
D
8 units
17

What are the x-intercepts of the graph of the function ? Use your graphing calculator to estimate the answer.

Question illustration
A
, where n is any integer
Option A
B
, where n is any integer
Option B
C
, where n is any integer
Option C
D
, where n is any integer
Option D
18

Where does the graph of the function have asymptotes?

Question illustration
A
at the values of x where
Option A
B
at the values of x where
Option B
C
at the values of x where is undefined
Option C
D
at the values of x where is undefined
Option D
19

What is the range of the function ?

Question illustration
A
all real numbers
B
all real numbers except , where n is any integer
Option B
C
all real numbers except , where n is any integer
Option C
D
all real numbers except , where n is any integer
Option D
20

Which is an asymptote of the graph of the function ?

Question illustration
A
mc020-2.jpg
Option A
B
mc020-3.jpg
Option B
C
mc020-4.jpg
Option C
D
mc020-5.jpg
Option D

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