MCPCalc

Visual Math

Unit Circle Explorer

A thorough unit-circle reference with exact angles, coordinate interpretation, and visual links between the circle, the right triangle, and the tangent line.

Scratchpad (not saved)

Exact-angle visualization

Trace the terminal side around the circle and watch cosine, sine, and tangent turn into geometry.

Quadrant 1Ref
Cosine line
Sine line
Tangent line
Select exact angle 0Select exact angle π/12Select exact angle π/6Select exact angle π/4Select exact angle π/3Select exact angle 5π/12Select exact angle π/2Select exact angle 7π/12Select exact angle 2π/3Select exact angle 3π/4Select exact angle 5π/6Select exact angle 11π/12Select exact angle πSelect exact angle 13π/12Select exact angle 7π/6Select exact angle 5π/4Select exact angle 4π/3Select exact angle 17π/12Select exact angle 3π/2Select exact angle 19π/12Select exact angle 5π/3Select exact angle 7π/4Select exact angle 11π/6Select exact angle 23π/12
θP

The green segment tracks x = cos(θ), the purple segment tracks y = sin(θ), and the orange dashed line is the tangent to the circle at the terminal point.

cos(θ)

sin(θ)

tan(θ)

sec(θ)

csc(θ)

cot(θ)

Terminal point

Cosine is the x-coordinate and sine is the y-coordinate on the unit circle.

Quadrant signs

sin, cos, and tan are all positive.

Reference-angle view

Exact values repeat by reference angle; only the quadrant signs change.