By Zencalcy Editorial TeamLast reviewed About us
The unit circle (radius 1) turns every angle into coordinates: cos(θ) is x, sin(θ) is y, tan(θ) is y/x. Enter any angle for all three values at once, and use the standard-angle table below for the classics.
cos, sin, and tan of any angle from the unit circle.
cos θ = x, sin θ = y, tan θ = y/x on the circle x² + y² = 1
| Symbol | Meaning |
|---|---|
| θ | Angle from the positive x-axis |
| (x, y) | Point on the unit circle |
θ = 45° → (√2/2, √2/2) ≈ (0.707107, 0.707107), tan = 1. Table: 0°→(1,0), 30°→(0.866025,0.5), 45°→(0.707107,0.707107), 60°→(0.5,0.866025), 90°→(0,1). tan(90°) is undefined.
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With r = 1, the trig ratios equal the coordinates directly — no division needed.
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Content updated: September 2026