The Amazing Unit Circle
Trigonometric Function Facts

The unit circle x2 + y2 = 1 is a mine of information about the trigonometric functions.

Roll over a link to see what the unit circle tells you about that aspect of the trigonometric functions.

Click to get more details about that topic.

unit circle

Nice angles (degrees)

Nice angles (radians)

Definition of sine & cosine

All six trig. functions as lengths

The fundamental trigonometric identity

Signs of sine, cosine and tangent, by quadrant

Reference angles, Quadrant II

Reference angles, Quadrant III

Reference angles, Quadrant IV

Periods of sine, cosine and tangent

Complementary angle identities

Supplementary angle identities

Phase shift identities

Opposite angle identities

Negative angle identities (symmetry of sine and cosine)

Now available: Amazing Unit Circle t-shirt shows identities (shirt front) and all six trigonometric functions as lengths (shirt back). It's a great gift for students and teachers.

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