Unit Circle Simulator

Move around the unit circle and watch sine, cosine, and tangent values update

Angle (degrees)

Unit Circle Formulas

Quantity	Formula	Meaning
Point	(x, y) = (cos theta, sin theta)	Coordinates of the terminal point.
Tangent	tan theta = sin theta / cos theta	Undefined when cos theta = 0.
Radians	radians = degrees x pi / 180	Converts degree measure to radian measure.

Unit Circle Rules

Cosine is the x-coordinate on the unit circle.
Sine is the y-coordinate on the unit circle.
Angles in quadrant I have positive sine and cosine values.
Angles on the vertical axis have undefined tangent because cosine is zero.

Example: at 45 degrees, cos theta and sin theta are both about 0.7071, so tan theta is about 1.

Common Unit Circle Values

Degrees	Radians	cos theta	sin theta	tan theta
0	0	1	0	0
30	pi / 6	sqrt(3) / 2	1 / 2	sqrt(3) / 3
45	pi / 4	sqrt(2) / 2	sqrt(2) / 2	1
60	pi / 3	1 / 2	sqrt(3) / 2	sqrt(3)
90	pi / 2	0	1	undefined

How to Read the Simulator

Move the angle and compare the point coordinates with the sine and cosine values.
Use the quadrant label to check whether sine, cosine, and tangent should be positive or negative.
Watch tangent near 90 degrees and 270 degrees, where the value becomes undefined.

Frequently Asked Questions

What is the unit circle?▼

The unit circle is a circle with radius 1 centered at the origin. A point on it has coordinates (cos theta, sin theta).

How do sine and cosine appear on the unit circle?▼

Cosine is the x-coordinate and sine is the y-coordinate of the terminal point.

What is tangent on the unit circle?▼

Tangent is sin(theta)/cos(theta), so it is undefined when cosine is zero.

Can this show radians and degrees?▼

Yes. The angle slider is in degrees, and the simulator also reports the radian measure.

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