Algebra 2 · Unit 10 · Topic 10.2
The Unit Circle and Sine and Cosine
On the unit circle, the point at angle θ from the positive x-axis is (cos θ, sin θ).
Definition and explanation
On the unit circle, the point at angle θ from the positive x-axis is (cos θ, sin θ). The coordinates satisfy cos²θ + sin²θ = 1, and quadrant location determines their signs.
Worked example
At θ = 5π/6, the reference angle is π/6 and the point is in quadrant II. Thus cos θ = −√3/2 and sin θ = 1/2. Squaring and adding gives 3/4 + 1/4 = 1.
Common mistake
A reference angle gives magnitudes, but the quadrant supplies the signs.
Key takeaway
On the unit circle, the point at angle θ from the positive x-axis is (cos θ, sin θ).
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.