How to read the unit circle
- Find an angle in degrees (60), radians (π/3) or by a value (√3).
- Read sin, cos and tan as exact values with decimals.
- Use the quadrant buttons to see how the signs change around the circle.
Where the exact values come from
The 45° values come from a right isosceles triangle with sides 1, 1 and √2, which gives √2/2. The 30° and 60° values come from half an equilateral triangle with sides 1, √3 and 2, which gives 1/2 and √3/2. Every other angle in the table is one of these reflected into another quadrant, which is why only the signs change.
Radians
A full turn is 2π radians, so 180° is π. Radians measure an angle by the arc length it cuts on the unit circle, which makes calculus formulas simpler: the derivative of sin x is cos x only when x is in radians.