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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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
3
Which equation can be used to determine the reference angle, r, if ?
A
r = theta
B
r = pi minus theta
C
r = theta minus pi
D
r = 2 pi minus theta
4
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
5
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
6
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
8
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.9
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)
10
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
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