AnswersFall 24 GMS Geometry Concepts and Connections BLaw of Sines (Sec 8-3)

The Unit Circle Answers

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1
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Which of the following best explains why ?

Question illustration
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
Cosine is positive in the second quadrant and negative in the fourth quadrant.
D
The angles do not have the same reference angle or the same sign.
2
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Which of the following is true of the values of x and y in the diagram below?

Question illustration
A
y < x
B
y > x
C
y + x = 1
D
StartFraction y Over x EndFraction = 1
Option D
3

Which expression is equivalent to ?

Question illustration
A
sine StartFraction pi Over 6 EndFraction
Option A
B
sine StartFraction 5 pi over 3 EndFraction
Option B
C
sine StartFraction 5 pi over 3 EndFraction
Option C
D
sine StartFraction 11 pi Over 6 EndFraction
Option D
4

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

A
180 degrees minus x
Option A
B
x minus 180 degrees
Option B
C
360 degrees minus x
Option C
D
x minus 360 degrees
Option D
5

For which value of is ?

Question illustration
A
StartFraction pi Over 2 EndFraction
Option A
B
Pi
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
2 pi
Option D
6

What is the value of in the unit circle below?

Question illustration
A
One-half
Option A
B
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option B
C
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option C
D
StartRoot 3 EndRoot
Option D
7

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

Question illustration
A
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option A
B
(one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
(StartFraction StartRoot 3 EndRoot Over 3 EndFraction, one-half)
Option C
D
(one-half, StartFraction StartRoot 3 EndRoot Over 3 EndFraction)
Option D
8

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

Question illustration
A
has a reference angle of 30° and is in Quadrant I or II
Option A
B
has a reference angle of 30° and is in Quadrant I or IV
Option B
C
has a reference angle of 60° and is in Quadrant I or II
Option C
D
has a reference angle of 60° and is in Quadrant I or IV
Option D
9

Which equation can be used to determine the reference angle, r, if ?

Question illustration
A
r = theta
Option A
B
r = pi minus theta
Option B
C
r = theta minus pi
Option C
D
r = 2 pi minus theta
Option D
10

On the unit circle, where , when is undefined?

Question illustration
A
and
Option A
B
sine theta = cosine theta
Option B
C
and
Option C
D
sin theta = StartFraction 1 Over cosine theta EndFraction
Option D
11

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

A
180 degrees minus x
Option A
B
x minus 180 degrees
Option B
C
360 degrees minus x
Option C
D
x minus 360 degrees
Option D
12

Which of the following best explains why ?

Question illustration
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
Cosine is positive in the second quadrant and negative in the fourth quadrant.
D
The angles do not have the same reference angle or the same sign.
13

What is the value of in the diagram below?

Question illustration
A
Three-fifths
Option A
B
Three-fourths
Option B
C
Four-fifths
Option C
D
Four-thirds
Option D
14

Which of the following best explains why ?

Question illustration
A
The angles do not have the same reference angle.
B
Tangent is positive in the second quadrant and negative in the fourth quadrant.
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.
15

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

Question illustration
A
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option A
B
(one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
(StartFraction StartRoot 3 EndRoot Over 3 EndFraction, one-half)
Option C
D
(one-half, StartFraction StartRoot 3 EndRoot Over 3 EndFraction)
Option D
16

What is the value of in the diagram below?

Question illustration
A
StartFraction 7 Over 25 EndFraction
Option A
B
StartFraction 7 Over 24 EndFraction
Option B
C
StartFraction 24 Over 25 EndFraction
Option C
D
StartFraction 24 Over 7 EndFraction
Option D
17

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

Question illustration
A
has a reference angle of 30° and is in Quadrant I or II
Option A
B
has a reference angle of 30° and is in Quadrant I or IV
Option B
C
has a reference angle of 60° and is in Quadrant I or II
Option C
D
has a reference angle of 60° and is in Quadrant I or IV
Option D
18

What is the reference angle for a 240° angle?

A
30°
B
60°
C
180°
D
270°
19

Which of the following explains why using the unit circle?

Question illustration
A
The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.
B
The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the x (sin) distance of a 30° angle is the same as the y (cos) distance of a 60° angle.
C
The ratios describe different sides of the same right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.
D
The ratios describe different sides of the same right triangle. On a unit circle, the x (sin) distance of a 30° angle is the same as the y (cos) distance of a 60° angle.
20

What is the value of in the unit circle below?

Question illustration
A
One-half
Option A
B
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option B
C
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option C
D
StartRoot 3 EndRoot
Option D

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