AnswersGA-Advanced Algebra Concepts and Connections CRUnit Test

The Unit Circle Answers

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1
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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
2
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The radius of the circle below intersects the unit circle at . What is the value of tan ?[Not drawn to scale]

Question illustration
A
mc009-4.jpg
Option A
B
mc009-5.jpg
Option B
C
mc009-6.jpg
Option C
D
mc009-7.jpg
Option D
3

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
4

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
5

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.
6

What is the reference angle for a 240° angle?

A
30°
B
60°
C
180°
D
270°
7

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.
8

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
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

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.
11

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
12

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
13

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
14

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
15

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.
16

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.
17

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

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