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Unit Circle

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The following diagram shows how the unit circle is related to sin, cos and tan. Scroll down the page for more examples and solutions on the unit circle, sine, cosine, and tangent.
Unit Circle sin cos tan

In some other lessons, we have covered the three common trigonometry functions sine, cosine and tangent using the basic SOH-CAH-TOA definition.

In this lesson, we will extend the definition of the trigonometry functions by using the unit circle.

A unit circle is a circle of radius one unit with its center at the origin.

Sine Function

As illustrated in the following diagram:
For a point (x, y) on the unit circle; sin θ = ⇒ sin θ = y




Cosine Function

As illustrated in the following diagram:
For a point (x, y) on the unit circle; cos θ = ⇒ cos θ = x

Tangent Function

As illustrated in the following diagram:
For a point (x, y) on the unit circle; tan θ =

Unit Circle - Angles from 0° to 360°. Angles from 0 to 2π Unit Circle - Points (x, y) along the unit circle The following video shows how the unit circle can be used in the definitions of sine, cosine and tangent.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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