Unit Circle Calculator

The unit circle is the single most important picture in trigonometry, a circle of radius one centred at the origin that ties angles directly to coordinates, and this calculator gives you the exact point on it for any angle you choose. Enter an angle in degrees or radians and it returns the coordinates where the angle meets the circle, which are simply the cosine and the sine of that angle, along with the tangent, the radian or degree equivalent, and the quadrant, all updating as you type. This is the heart of why the unit circle matters: the x-coordinate of the point is the cosine and the y-coordinate is the sine, so the abstract trig functions become something you can see and place. At 0 degrees the point sits at (1, 0); at 90 degrees it climbs to (0, 1); at 60 degrees it rests at (0.5, 0.866); and as the angle sweeps right around, the coordinates trace out the familiar wave shapes of sine and cosine. The tangent, the y-coordinate divided by the x-coordinate, shoots off to infinity at 90 and 270 degrees where the cosine is zero, which the calculator flags as undefined. Seeing the radian measure beside the degrees also helps cement the link between the two, with a full turn being 2 pi radians. That makes the tool genuinely useful for senior school and first-year university students learning trigonometry, evaluating functions, understanding signs in each quadrant, and preparing for tests where the unit circle is everything. Because the coordinates update live, you can move the angle around and watch the point travel the circle while sine and cosine rise and fall. The relationships and a worked example are explained clearly below.

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