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The Unit Circle Definition of Trigonometric Function

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Examples, solutions, videos, worksheets, games, and activities to help Algebra II students learn the unit circle definition of trigonometric function.

The Definitions of Sine and Cosine
The right triangle definitions of sine and cosine only apply to acute angles, so a more complete definition is needed. The point where the terminal side intersects the unit circle (x, y) is the basis for this definition. Since the radius (and therefore hypotenuse of the right triangle) is 1, the denominators cosine = adjacent/hypotenuse and sine = opposite/hypotenuse are also 1. Thus, the definition is y = sine and x = cosine.

The following diagram shows the unit circle definition of the trig functions: sin, cos, and tan. Scroll down the page for more examples and solutions on the unit circle and trigonometry.
Unit Circle trigonometry

Unit Circle Definition of Trig Functions
Using the unit circle to define the sine, cosine, and tangent functions The unit circle definition of trigonometric function
Using the unit circle to extend the SOH CAH TOA definition of the basic trigonometric functions.

Deriving Values on the Unit Circle.
This video shows how to derive the values in the first quadrant of the unit circle.
A Trick to Remember Values on The Unit Circle
This video shows a little 'trick' to remember the values on the unit circle in the first quadrant. A way to remember the Entire Unit Circle for Trigonometry.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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