The Unit Circle Answers
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1
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For which value of is ?
A
StartFraction pi Over 2 EndFraction
B
Pi
C
StartFraction 3 pi Over 2 EndFraction
D
2 pi
2
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Which expression is equivalent to ?
A
sine StartFraction pi Over 6 EndFraction
B
sine StartFraction 5 pi over 3 EndFraction
C
sine StartFraction 5 pi over 3 EndFraction
D
sine StartFraction 11 pi Over 6 EndFraction
3
What is the value of in the diagram below?
A
Three-fifths
B
Three-fourths
C
Four-fifths
D
Four-thirds
4
Which of the following is true of the location of the terminal side of an angle, , whose sine value is ?
A
has a reference angle of 30° and is in Quadrant I or II
B
has a reference angle of 30° and is in Quadrant I or IV
C
has a reference angle of 60° and is in Quadrant I or II
D
has a reference angle of 60° and is in Quadrant I or IV
5
What is the reference angle for a 240° angle?
A
30°B
60°C
180°D
270°6
Which of the following explains why using the unit circle?
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.7
Which of the following best explains why ?
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.8
The terminal side of an angle measuring radians intersects the unit circle at what point?
A
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
B
(one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
C
(StartFraction StartRoot 3 EndRoot Over 3 EndFraction, one-half)
D
(one-half, StartFraction StartRoot 3 EndRoot Over 3 EndFraction)
9
What is the value of in the diagram below?
A
StartFraction 7 Over 25 EndFraction
B
StartFraction 7 Over 24 EndFraction
C
StartFraction 24 Over 25 EndFraction
D
StartFraction 24 Over 7 EndFraction
10
What is the value of in the unit circle below?
A
One-half
B
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
C
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
D
StartRoot 3 EndRoot
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