Interactive Unit Circle Simulator
Interactive Unit Circle M(cos α; sin α)
Drag point M on the circle, move the slider or type an angle. The blue segment on the Ox axis is cos α, the red segment on the Oy axis is sin α; the tangent axis (x = 1) and the cotangent axis (y = 1) show tan α and cot α.
Tap or drag on the figure to move M. When the figure has focus, the arrow keys change the angle by 1°; hold Shift for 15°.
The simulator above lets you drag point M around the unit circle and read the cosine, sine, tangent, cotangent, and quadrant of the angle in real time.
Formulas used
M(cos α; sin α), cos²α + sin²α = 1
- The x-coordinate of M is cos α, the y-coordinate is sin α.
- Quadrant I: all positive. Quadrant II: sin positive. Quadrant III: tan positive. Quadrant IV: cos positive.
Worked example
For α = 135° (quadrant II):
M(−√2/2; √2/2), tan α = −1
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Drag point M or type an angle in degrees or radians.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.