The Unit Circle Answers
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1
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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.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 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.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
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
6
Which of the following is true of the values of x and y in the diagram below?
A
y < xB
y > xC
y + x = 1D
StartFraction y Over x EndFraction = 1
7
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
8
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
9
For which value of is ?
A
StartFraction pi Over 2 EndFraction
B
Pi
C
StartFraction 3 pi Over 2 EndFraction
D
2 pi
10
The radius of the circle below intersects the unit circle at . What is the value of tan ?[Not drawn to scale]
A
mc009-4.jpg
B
mc009-5.jpg
C
mc009-6.jpg
D
mc009-7.jpg
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