
Precalculus Sine and Cosine Function Values on Unit Circle
Authored by Anthony Clark
Mathematics
12th Grade
CCSS covered
Used 1+ times

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20 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point S, and point P also lies on the circle. The coordinates of P are (x, y), and the coordinates of S are (x, -y). Which of the following is true about the sine of θ?
sin θ = x/5, because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.
sin θ = -x/5, because it is the ratio of the horizontal displacement of S from the y-axis to the distance between the origin and S.
sin θ = -y/5, because it is the ratio of the vertical displacement of S from the x-axis to the distance between the origin and S.
sin θ = y/5, because it is the ratio of the vertical displacement of P from the x-axis to the distance between the origin and P.
Tags
CCSS.HSF.TF.A.2
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The figure above shows a circle of radius 5 along with the equilateral triangle P̂QO. Which of the following gives the coordinates of point P?
[5 cos(5π/6), 5 sin(5π/6)]
[5 cos(7π/3), 5 sin(7π/3)]
[5 cos(2π/3), 5 sin(2π/3)]
[5 cos(4π/3), 5 sin(4π/3)]
Tags
CCSS.HSF.TF.B.7
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point R, and point S also lies on the circle. The coordinates of R are (-x, y), and the coordinates of S are (x, y). Which of the following is true about the cosine of θ?
cos θ = -x/8, because it is the ratio of the horizontal displacement of R from the y-axis to the distance between the origin and R.
cos θ = x/8, because it is the ratio of the horizontal displacement of S from the y-axis to the distance between the origin and S.
cos θ = -y/8, because it is the ratio of the vertical displacement of R from the x-axis to the distance between the origin and R.
cos θ = y/8, because it is the ratio of the vertical displacement of S from the x-axis to the distance between the origin and S.
Tags
CCSS.HSF.TF.A.2
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point P, and point R also lies on the circle. The coordinates of P are (x, y) and the coordinates of R are (x, -y). Which of the following is true about the tangent of θ?
tan θ = y/x, because it is the ratio of the vertical displacement of P to the horizontal displacement of P.
tan θ = x/y, because it is the ratio of the horizontal displacement of P to the vertical displacement of P.
tan θ = -y/x, because it is the ratio of the vertical displacement of R to the horizontal displacement of R.
tan θ = -x/y, because it is the ratio of the horizontal displacement of R to the vertical displacement of R.
Tags
CCSS.HSF.TF.A.2
5.
MULTIPLE SELECT QUESTION
1 min • 1 pt
What quadrant is sine negative in? Choose 2.
I
II
III
IV
Tags
CCSS.HSF.TF.A.2
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The sine of any angle on the unit circle is the y-coordinate.
True
False
Tags
CCSS.HSF.TF.A.2
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
To find the (x, y) coordinates on the unit circle at at any angle, use
(tan, cot)
(cot, tan)
(sin, cos)
(cos, sin)
Tags
CCSS.HSF.TF.A.2
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