Every angle has a story.
Follow a point around the circle. Watch sine, cosine, and tangent connect.
Make an angle. See the connection.
Quadrant I · both coordinates are positive.
One circle. Three trigonometric functions.
The unit circle has a radius of 1. Starting at the positive x-axis, an angle θ moves counterclockwise around the circle. The point you land on is (cos θ, sin θ). Tangent is the ratio sin θ / cos θ, so it is undefined where cosine is zero.
Use the number field or arrow keys on the slider for precise, keyboard-accessible exploration. Special angles show exact values alongside decimal approximations.
Unit circle questions
Wondering about the why? Start here.
How does the unit circle show sine and cosine?
A unit circle has radius 1. Measure an angle counterclockwise from the positive x-axis: the point on the circle has coordinates (cos θ, sin θ). Its horizontal coordinate is cosine and its vertical coordinate is sine.
Connect the trigonometric ratiosWhy is tangent undefined at 90° and 270°?
Tangent is sin θ divided by cos θ. At 90° and 270°, cosine is zero, so the ratio would divide by zero. The explorer displays “undefined” at those angles.
Explore sine and cosine graphsWhat is the difference between degrees and radians?
Both measure angles. A full turn is 360° or 2π radians, so 180° equals π radians. Multiply degrees by π/180 to convert to radians; multiply radians by 180/π to convert to degrees.
Convert degrees and radians