Unit Circle Calculator
Look up the trigonometric values for any angle on the unit circle. Enter an angle in degrees to find its radian equivalent, sine, cosine, tangent, reference angle, and quadrant.
The unit circle is a circle with radius 1 centered at the origin. Every angle θ maps to a point (cos θ, sin θ) on this circle, which is why the unit circle is the foundation of trigonometry. The x-coordinate gives cosine and the y-coordinate gives sine.
A reference angle is the acute angle that the terminal side of an angle makes with the x-axis. For angles in Quadrant I the reference angle equals the angle; in Quadrant II it is 180° minus the angle; in Quadrant III it is the angle minus 180°; and in Quadrant IV it is 360° minus the angle. The trig function values of any angle equal plus or minus the values of its reference angle, with the sign determined by the quadrant.
The unit circle provides a visual way to remember which trig functions are positive in each quadrant. In Quadrant I all are positive, in Quadrant II only sine is positive, in Quadrant III only tangent is positive, and in Quadrant IV only cosine is positive (the mnemonic All Students Take Calculus).