Unit Circle
Interactive unit circle with sin, cos, tan and exact values for every angle.
About this tool
Drag around the circle, use the slider or type an angle in degrees. The point, its cosine (green) and sine (red) are drawn, and the panel shows the angle in radians, the exact and decimal values of sin, cos and tan, and the quadrant. Dragging snaps to the standard angles. Open the table for exact values of every multiple of 30° and 45°.
How the unit circle defines trigonometry
The unit circle is a circle of radius 1 centred at the origin. For any angle θ measured anticlockwise from the positive x-axis, the point where the angle's ray meets the circle has coordinates (cos θ, sin θ), and tan θ = sin θ ÷ cos θ is the slope of that ray. This definition extends trigonometry from the acute angles of a right triangle to any angle, positive or negative, and explains why the functions repeat every 360°, or 2π radians. The exact values come from two special triangles. A 45-45-90 triangle with hypotenuse 1 has legs √2/2, so sin 45° = cos 45° = √2/2. Halving an equilateral triangle gives a 30-60-90 triangle with sides 1/2, √3/2 and 1, so sin 30° = 1/2 and cos 30° = √3/2. Every other standard angle reuses these values with signs set by the quadrant: all functions are positive in quadrant I, sine in II, tangent in III and cosine in IV, often remembered as "All Students Take Calculus". To convert, radians = degrees × π ÷ 180, so 30° is π/6 and 90° is π/2. Tangent is undefined at 90° and 270°, where cos θ = 0. The triangle solver, the scientific calculator and the Pythagorean theorem calculator are related.
Frequently asked questions
What is sin 30 degrees?
1/2. Cos 30° is √3/2 and tan 30° is √3/3.
How do you convert degrees to radians?
Multiply by π and divide by 180: 60° = π/3 radians.
Why is tan 90 undefined?
tan θ = sin θ ÷ cos θ, and cos 90° = 0, so the division is undefined.
Is my data saved?
No. Everything runs in your browser and nothing is stored or sent.