The Unit Circle Answers
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1
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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
2
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What is the value of in the diagram below?
A
Three-fifths
B
Three-fourths
C
Four-fifths
D
Four-thirds
3
What is the reference angle for a 240° angle?
A
30°B
60°C
180°D
270°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
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
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 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
9
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
10
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
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