Trigonometry/The unit circle

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The Unit Circle is a circle with its center at the origin (0,0) and a radius of one unit.

Angles are always measured from the positive x-axis (also called the "right horizon"). Angles measured counterclockwise have positive values; angles measured clockwise have negative values.

A unit circle with certain exact values marked on it is below:

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It is well worth the effort to memorize the values of sine and cosine on the unit circle (cosine is equal to x while sine is equal to y) included in this unit circle, since the information will be useful for many math concepts.

Unit circles form the basis of most analog clocks and animations on computers since the cos and sin correspond to the x and y positions of the end of the line segments representing the hands of the clock. The angle of a hand is calculated (-6° or -π/30 radians per hour, minute or second past the 3 position on the clock, depending on the hand) and the cosine and sine of the angle are used to calculate the co-ordinates of the end point of the hand.

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