AnswersS1S-OC Pre-Calculus A E3700 - AGInverse 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

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