Worked example
An angle measures 0 radians. What is its exact sine?
Answer & why
Answer: 0
On the unit circle, sine is the vertical coordinate. At 0 radians that coordinate is 0, so sin(0) = 0.
Grade 12 · Math
Read exact sine values on the unit circle
Use a unit-circle point’s vertical coordinate to determine sine, including its sign.
6 authored questions + worked example
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All questions
All 6 authored questions for this skill.
Question 1
An angle measures π/2 radians. What is its exact sine?
- 0
- 1
- −1
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer: 1
On the unit circle, sine is the vertical coordinate. At π/2 radians that coordinate is 1, so sin(π/2) = 1.
Question 2
An angle measures π radians. What is its exact sine?
- −1
- 0
- 1
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer: 0
On the unit circle, sine is the vertical coordinate. At π radians that coordinate is 0, so sin(π) = 0.
Question 3
An angle measures 7π/6 radians. What is its exact sine?
- −1
- 0
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer:
On the unit circle, sine is the vertical coordinate. At 7π/6 radians that coordinate is , so sin(7π/6) = −1/2.
Question 4
An angle measures 3π/2 radians. What is its exact sine?
- 0
- −1
- 1
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer: −1
On the unit circle, sine is the vertical coordinate. At 3π/2 radians that coordinate is −1, so sin(3π/2) = −1.
Question 5
An angle measures 0 radians. What is its exact sine?
- 0
- −1
- 1
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer: 0
On the unit circle, sine is the vertical coordinate. At 0 radians that coordinate is 0, so sin(0) = 0.
Question 6
An angle measures π/6 radians. What is its exact sine?
- 1
- 0
A hint
Locate the angle on the unit circle and use its y-coordinate, including the sign.
Answer & why
Answer:
On the unit circle, sine is the vertical coordinate. At π/6 radians that coordinate is , so sin(π/6) = 1/2.