Interactive unit circle: drag the angle and see sin, cos, tan values update live. Visual trigonometry learning.
Move the point around the unit circle to set an angle.
See sine, cosine, tangent, and other values update in real time.
Observe how angle changes affect all trigonometric functions.
The Unit Circle Explorer draws a circle of radius 1 centered on the origin and places a movable point on its rim. Drag the point, or type an angle, and the tool reads the point's coordinates as cosine and sine, then divides them for tangent, updating all three live. The surprise most users hit first: the angle is measured counterclockwise from the positive x-axis, so 0 degrees sits at 3 o'clock, not 12. And the coordinates come out as (cos, sin) - the horizontal value is cosine, the vertical value is sine - which is easy to get backwards.
A concrete input and expected output from the current implementation.
Input
Set the angle to 30 degrees (drag the point to the 30-degree mark).
Expected output
cos 30 degrees = 0.866, sin 30 degrees = 0.5, tan 30 degrees = 0.577. The point sits at (0.866, 0.5).
On a unit circle the point at angle theta is exactly (cos theta, sin theta). At 30 degrees the 30-60-90 triangle gives sin = 1/2 and cos = sqrt(3)/2, and tan = sin / cos = 1/sqrt(3), which rounds to 0.577.
Every point on a circle of radius 1 has coordinates (cos theta, sin theta) for some angle theta measured counterclockwise from the positive x-axis. Dragging the point along the rim changes theta, so the readout is a live table of trig values. Tangent is not a coordinate of the point: it is the ratio sin / cos, shown as a third value.
In quadrant I (0-90 degrees) both coordinates are positive; in quadrant II (90-180) sine stays positive while cosine turns negative, so tangent - the ratio - turns negative too. The pattern mirrors through quadrants III and IV. At exactly 90 and 270 degrees, cosine is zero and tangent is undefined; the readout has no finite value to show there.
Tangent is sin divided by cos, and cos approaches zero as the angle approaches 90 degrees, so the ratio grows without bound. Just past 90 degrees, cos is negative while sin is still positive, so tan jumps from huge positive to huge negative; it is not continuous across 90 degrees. At exactly 90 degrees, tan is undefined.
Sine is the vertical coordinate of the point on the circle. The points at 30 and 150 degrees sit at the same height above the x-axis, so their y-coordinates - and therefore their sine values - match. Their x-coordinates have opposite signs, which is why cos 150 degrees equals -cos 30 degrees.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Interactive periodic table - click elements, enter quiz mode, and guess elements from their properties. Gamified learning.
Explore the periodic table with element details, properties, and category filtering.
Browse and search ASCII, Unicode, and binary character codes with copy-to-clipboard.
Test your knowledge of semantic HTML elements with quizzes and best-practice tips.
Structured typing lessons with finger placement guide. Track WPM improvement over time with localStorage persistence.
Timed multiplication drills with accuracy tracking per table (1-12). Progress chart saved across sessions.