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Home/Math Visualization/Trigonometry Circle

Trigonometry Circle

Unit circle with angle θ: read sin θ, cos θ, and tan θ as coordinates and ratios. Links rotation to trigonometric functions used in waves and E&M phasors.

Who it's for: Precalculus and intro physics math support.

Key terms

  • unit circle
  • sine
  • cosine
  • tangent
  • radians

Angle

40°

Shortcuts

  • •Tip: drag θ to see sin, cos, tan

Measured values

sin θ0.6428
cos θ0.7660
tan θ0.8391

How it works

On the unit circle, cos θ is the x-coordinate and sin θ is the y-coordinate of the point at angle θ from the positive x-axis. The diagram shows a circle of radius R in pixels; ratios match the unit circle.

Key equations

cos θ = x,   sin θ = y,   tan θ = sin θ / cos θ