Precalculus Sine and Cosine Function Values on Unit Circle

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.

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)]

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.

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.

What quadrant is sine negative in? Choose 2.

• I

• II

• III

• IV

The sine of any angle on the unit circle is the y-coordinate.

• True

• False

To find the (x, y) coordinates on the unit circle at at any angle, use

• (tan, cot)

• (cot, tan)

• (sin, cos)

• (cos, sin)

• 
• 
• 
• 

Which angle satisfies the equation cosx = 0? Select all that apply

• x = π/2

• x = π

• x = 240º

• x = 270º

• 1/2

• undefined-1