How do I move the point on the circle?

Click and drag the blue point anywhere on or near the circle. On touch devices, touch and drag works the same way. The angle and trig values update in real time as you drag.

What are the special angles?

The special angles are 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, and 330° (and the equivalents in radians). These are highlighted because their sin, cos, and tan values are exact fractions or simple roots.

What does the reference triangle show?

The reference triangle draws the right triangle formed by the point, its projection onto the x-axis, and the origin. The horizontal leg represents cos θ and the vertical leg represents sin θ.

Why does tan θ show 'undefined' at some angles?

Tangent is undefined at 90° and 270° (π/2 and 3π/2 radians) because cos θ = 0 at those angles and tan θ = sin θ / cos θ would require dividing by zero.

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Unit Circle

Interactive unit circle with draggable point, sin/cos/tan display

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关于此工具

An interactive canvas-based unit circle for learning and teaching trigonometry. Drag the point around the circle to any angle and instantly see the exact degree value, the radian equivalent, and the numeric values of sin θ, cos θ, and tan θ. Special angles (0°, 30°, 45°, 60°, 90°, and their equivalents in all four quadrants) are highlighted with their exact fractional values (e.g. sin 30° = ½). Toggle grid lines, axis labels, the reference right triangle, and exact-value annotations on or off to suit your study needs.

使用方法

1 Drag the blue point around the circle to any angle.
2 Read the angle in degrees and radians, plus the sin, cos, and tan values in the info panel.
3 When near a special angle, the exact fractional value is shown automatically.
4 Use the toggle buttons to show or hide the grid, axis labels, and reference triangle.
5 Click a special angle button to snap the point to that exact angle.

关于此工具

使用方法

常见问题