AnswersIC Pre-Cal - DeeringInverse Trigonometric Functions

Inverse Trigonometric Functions Answers

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The water level at a pier is modeled by the function , where y represents the water level measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.

Question illustration
A
1.6 hours
B
3.1 hours
C
14.4 hours
D
19.6 hours
2
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Which statement is true about y = arctanx?

A
The domain is .
Option A
B
The range is all real numbers.
C
The graph contains vertical asymptotes.
D
The graph is symmetric about the origin.
3

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
4

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
(–∞, ∞)
5

Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
6

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
7

Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
8

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
9

Which expression is undefined?

A
sin-1(1)
B
sin-1(–2)
C
cos-1(0)
D
cos-1(–1)
10

What is the value of sin-1(1)?

A
Negative StartFraction pi Over 2 EndFraction
Option A
B
0
C
StartFraction pi Over 2 EndFraction
Option C
D
π

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