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The Trig Functions and the Unit Circle

Diagram of the unit circle, with the 6 trig functions shown as lengths

Each of the six trig functions can be thought of as a length related to the unit circle.

The sine and cosine functions are distances from the unit circle to the axes.

The tangent and cotangent functions are the lengths of lines tangent to the unit circle from the axis to the ray sweeping out the angle.

The secant and cosecant functions are lengths of the ray, or secant line, from the origin to its intersection with the tangent lines.

Just for fun: Here are all of the graphics combined. I always seem to make this "mistake" every time I create animations. But it could also be an instructive diagram.