The Unit Circle

exact values
Angle θ
0°
Quadrantal · reference 0°
0
Six functions
cos θ11.0000
sin θ00.0000
tan θ00.0000
sec θ11.0000
csc θ——
cot θ——
Point on circle(1, 0)
Coterminal360° · −360°
Where functions stay positive
II
sin csc
I
all
III
tan cot
IV
cos sec
Where the values come from
1 1 √2 45° 45° √3 1 2 30° 60°
cos²θ + sin²θ = 1  ·  tan θ = sin θ ⁄ cos θ
sin(−θ) = −sin θ  ·  cos(−θ) = cos θ
sec = 1⁄cos  ·  csc = 1⁄sin  ·  cot = 1⁄tan
Every angle repeats every 2π (360°).
Click any angle to pin it. Drag anywhere on the circle to sweep a free angle. ←→ step between special angles, Home returns to 0°.