AnswersPrecalculusInverse Trigonometric Functions

Inverse Trigonometric Functions — Quiz Answers

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For what value of theta is cosine inverse of open paren the fraction with numerator square root of 2 and denominator 2 close paren is equal to theta ?

A
pi over 4
B
pi over 6
C
pi over 2
D
pi over 3
2
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What is the value of sine inverse of 1 ?

A
pi
B
0
C
negative pi over 2
D
pi over 2
3

What is the domain of y is equal to inverse cosine x ?

A
left bracket negative 1 comma 1 right bracket
B
left bracket 0 comma pi right bracket
C
open paren negative infinity comma infinity close paren
D
left bracket negative pi over 2 comma pi over 2 right bracket
4

Which statement is true about y is equal to arctan x ?

A
The range is all real numbers.
B
The graph contains vertical asymptotes.
C
The domain is open paren negative mathrm pi over 2 comma mathrm pi over 2 close paren .
D
The graph is symmetric about the origin.
5

The average daily high temperature in Madrid peaks at 92 times degree F in the summer and drops as low as 33 times degree F in the winter. The temperature can be modeled by cap t times d is equal to 29 point 5 cosine open paren 2 pi over 365 times open paren d minus 204 close paren close paren plus 62 point 5 , 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 times degree F ?

A
63
B
204
C
106
D
270
6

Which trigonometric functions have the same maximum value?

A
y is equal to arctan x and y is equal to operatorname ar cs e c x
B
y is equal to arcsin x and y is equal to arctan x
C
y is equal to arcsin x and y is equal to arccos x
D
y is equal to arccos x and y is equal to operatorname ar cs e c x
7

What is the range of y is equal to inverse sine x ?

A
left bracket 0 comma pi right bracket
B
open paren negative infinity comma infinity close paren
C
left bracket negative pi over 2 comma pi over 2 right bracket
D
left bracket negative 1 comma 1 right bracket
8

Which graph represents y is equal to inverse tangent x ?

A
Image with description 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.
B
Image with description 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.
C
Image with description 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.
D
Image with description 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.
9

What is the value of sine inverse of cosine of open paren 2 pi over 3 close paren ?

A
the fraction with numerator negative 2 pi and denominator 3
B
negative pi over 6
C
pi over 6
D
2 pi over 3
10

Which expression is undefined?

A
sine inverse of negative 2
B
cosine inverse of 0
C
cosine inverse of negative 1
D
sine inverse of 1

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