AnswersPrecalculusThe Unit Circle

The Unit Circle — Quiz Answers

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Which of the following explains why cosine 60 degrees is equal to sine 30 degrees using the unit circle?

A
The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.
B
The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.
C
The ratios describe different sides of the same right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.
D
The ratios describe different sides of the same right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.
22
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Which of the following explains why cosine 60 degrees is equal to sine 30 degrees using the unit circle?

A
The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.
B
The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.
C
The ratios describe different sides of the same right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.
D
The ratios describe different sides of the same right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.
23

Which of the following best explains why cosine 2 pi over 3 is not equal to cosine 5 pi over 3 ?

A
The angles do not have the same reference angle.
B
Cosine is negative in the second quadrant and positive in the fourth quadrant.
C
The angles do not have the same reference angle or the same sign.
D
Cosine is positive in the second quadrant and negative in the fourth quadrant.
24

Which of the following best explains why cosine 2 pi over 3 is not equal to cosine 5 pi over 3 ?

A
Cosine is positive in the second quadrant and negative in the fourth quadrant.
B
The angles do not have the same reference angle or the same sign.
C
Cosine is negative in the second quadrant and positive in the fourth quadrant.
D
The angles do not have the same reference angle.
25

Which of the following is true of the location of the terminal side of an angle, theta , whose sine value is 1 half ?

A
theta has a reference angle of 30 degrees and is in Quadrant I or II
B
theta has a reference angle of 60 degrees and is in Quadrant I or IV
C
theta has a reference angle of 60 degrees and is in Quadrant I or II
D
theta has a reference angle of 30 degrees and is in Quadrant I or IV
26

Which expression is equivalent to sine 7 pi over 6 ?

A
sine 11 pi over 6
B
sine 5 pi over 6
C
sine 5 pi over 3
D
sine pi over 6
27

Which of the following best explains why tangent 5 pi over 6 is not equal to tangent 5 pi over 3 ?

A
Tangent is negative in the second quadrant and positive in the fourth quadrant.
B
Tangent is positive in the second quadrant and negative in the fourth quadrant.
C
The angles do not have the same reference angle.
D
The angles do not have the same reference angle or the same sign.
28

What is the reference angle for a 240 degrees angle?

A
30 degrees
B
270 degrees
C
60 degrees
D
180 degrees
29

On the unit circle, where 0 is less than theta comma theta is less than or equal to 2 pi , when is tangent theta undefined?

A
theta is equal to pi over 2 and theta is equal to 3 pi over 2
B
sine theta is equal to cosine theta
C
sine theta is equal to 1 over cosine theta
D
theta is equal to pi and theta is equal to 2 pi
30

The terminal side of an angle measuring pi over 6 radians intersects the unit circle at what point?

A
open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren
B
open paren the fraction with numerator square root of 3 and denominator 3 comma 1 half close paren
C
open paren 1 half comma the fraction with numerator square root of 3 and denominator 3 close paren
D
open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
31

Which expression can be used to determine the reference angle for an angle, x , measuring 150 degrees ?

A
360 degrees minus x
B
x minus 180 degrees
C
x minus 360 degrees
D
180 degrees minus x
32

Which of the following is true of the location of the terminal side of an angle, theta , whose sine value is 1 half ?

A
theta has a reference angle of 60 degrees and is in Quadrant I or IV
B
theta has a reference angle of 30 degrees and is in Quadrant I or IV
C
theta has a reference angle of 60 degrees and is in Quadrant I or II
D
theta has a reference angle of 30 degrees and is in Quadrant I or II
33

On the unit circle, where 0 is less than theta comma theta is less than or equal to 2 pi , when is tangent theta undefined?

A
sine theta is equal to cosine theta
B
theta is equal to pi over 2 and theta is equal to 3 pi over 2
C
theta is equal to pi and theta is equal to 2 pi
D
sine theta is equal to 1 over cosine theta
34

The terminal side of an angle measuring pi over 6 radians intersects the unit circle at what point?

A
open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
B
open paren the fraction with numerator square root of 3 and denominator 3 comma 1 half close paren
C
open paren 1 half comma the fraction with numerator square root of 3 and denominator 3 close paren
D
open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren
35

Which equation can be used to determine the reference angle, r , if theta is equal to 7 pi over 12 ?

A
r is equal to pi minus theta
B
r is equal to theta
C
r is equal to 2 pi minus theta
D
r is equal to theta minus pi
36

Which equation can be used to determine the reference angle, r , if theta is equal to 7 pi over 12 ?

A
r is equal to theta
B
r is equal to 2 pi minus theta
C
r is equal to pi minus theta
D
r is equal to theta minus pi
37

On the unit circle, where 0 is less than theta comma theta is less than or equal to 2 pi , when is tangent theta undefined?

A
sine theta is equal to 1 over cosine theta
B
sine theta is equal to cosine theta
C
theta is equal to pi and theta is equal to 2 pi
D
theta is equal to pi over 2 and theta is equal to 3 pi over 2
38

Which expression can be used to determine the reference angle for an angle, x , measuring 150 degrees ?

A
x minus 360 degrees
B
180 degrees minus x
C
360 degrees minus x
D
x minus 180 degrees
39

Which of the following is true of the location of the terminal side of an angle, theta , whose sine value is 1 half ?

A
theta has a reference angle of 30 degrees and is in Quadrant I or II
B
theta has a reference angle of 60 degrees and is in Quadrant I or II
C
theta has a reference angle of 30 degrees and is in Quadrant I or IV
D
theta has a reference angle of 60 degrees and is in Quadrant I or IV
40

Which of the following best explains why tangent 5 pi over 6 is not equal to tangent 5 pi over 3 ?

A
Tangent is negative in the second quadrant and positive in the fourth quadrant.
B
The angles do not have the same reference angle.
C
The angles do not have the same reference angle or the same sign.
D
Tangent is positive in the second quadrant and negative in the fourth quadrant.

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