The Unit Circle Answers
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1
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On the unit circle, where , when is undefined?
A
and
B
sine theta = cosine theta
C
and
D
sin theta = StartFraction 1 Over cosine theta EndFraction
2
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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
3
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
4
Which of the following best explains why ?
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.5
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.6
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)
7
What is the value of in the diagram below?
A
Three-fifths
B
Three-fourths
C
Four-fifths
D
Four-thirds
8
For which value of is ?
A
StartFraction pi Over 2 EndFraction
B
Pi
C
StartFraction 3 pi Over 2 EndFraction
D
2 pi
9
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.10
Which expression can be used to determine the reference angle for an angle, x, measuring 150°?
A
180 degrees minus x
B
x minus 180 degrees
C
360 degrees minus x
D
x minus 360 degrees
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