AnswersPrecalculusThe Unit Circle

The Unit Circle — Quiz Answers

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1
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Which expression can be used to determine the reference angle for an angle, x , measuring 150 degrees ?

A
360 degrees minus x
B
180 degrees minus x
C
x minus 360 degrees
D
x minus 180 degrees
2
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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
3

Which expression is equivalent to sine 7 pi over 6 ?

A
sine 5 pi over 6
B
sine pi over 6
C
sine 11 pi over 6
D
sine 5 pi over 3
4

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
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
The angles do not have the same reference angle.
5

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 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 30 degrees and is in Quadrant I or II
6

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

A
The angles do not have the same reference angle or the same sign.
B
Tangent is negative in the second quadrant and positive in the fourth quadrant.
C
Tangent is positive in the second quadrant and negative in the fourth quadrant.
D
The angles do not have the same reference angle.
7

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

A
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.
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 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.
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.
8

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 minus pi
B
r is equal to 2 pi minus theta
C
r is equal to theta
D
r is equal to pi minus theta
9

What is the reference angle for a 240 degrees angle?

A
60 degrees
B
30 degrees
C
180 degrees
D
270 degrees
10

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 and theta is equal to 2 pi
B
theta is equal to pi over 2 and theta is equal to 3 pi over 2
C
sine theta is equal to 1 over cosine theta
D
sine theta is equal to cosine theta
11

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

A
Tangent is positive in the second quadrant and negative in the fourth quadrant.
B
The angles do not have the same reference angle.
C
Tangent is negative in the second quadrant and positive in the fourth quadrant.
D
The angles do not have the same reference angle or the same sign.
12

Which expression is equivalent to sine 7 pi over 6 ?

A
sine 5 pi over 6
B
sine 5 pi over 3
C
sine 11 pi over 6
D
sine pi over 6
13

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
14

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 1 half comma the fraction with numerator square root of 3 and denominator 3 close paren
C
open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren
D
open paren the fraction with numerator square root of 3 and denominator 3 comma 1 half close paren
15

What is the reference angle for a 240 degrees angle?

A
30 degrees
B
180 degrees
C
270 degrees
D
60 degrees
16

Which expression is equivalent to sine 7 pi over 6 ?

A
sine 11 pi over 6
B
sine 5 pi over 3
C
sine 5 pi over 6
D
sine pi over 6
17

What is the reference angle for a 240 degrees angle?

A
30 degrees
B
60 degrees
C
270 degrees
D
180 degrees
18

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
19

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 or the same sign.
B
The angles do not have the same reference angle.
C
Cosine is positive in the second quadrant and negative in the fourth quadrant.
D
Cosine is negative in the second quadrant and positive in the fourth quadrant.
20

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

A
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.
B
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.
C
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.
D
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.

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