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Unit circle




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The Unit Circle can be used to model every Trigonometric function.

In mathematics, a unit circle is a circle with a radius of 1. The equation of the unit circle is [math]x^2 + y^2 = 1[/math]. The unit circle is centered at the Origin, or coordinates (0,0). It is often used in Trigonometry.

Trigonometric functions in the unit circle

In a unit circle, where [math]t[/math] is the angle desired, [math]x[/math] and [math]y[/math] can be defined as [math]\cos (t) = x[/math] and [math]\sin (t) = y[/math]. Using the function of the unit circle, [math]x^2 + y^2 = 1[/math], another equation for the unit circle is found, [math]\cos^2(t) + \sin^2(t) = 1[/math]. When working with trigonometric functions, it is mainly useful to use angles with measures between 0 and [math]\pi\over 2[/math] radians, or 0 through 90 degrees. It is possible to have higher angles than that, however. Using the unit circle, two identities can be found: [math]\cos (t) = \cos (2 \cdot \pi k + t)[/math] and [math]sin (t) = \sin (2 \cdot \pi k + t)[/math] for any integer [math]k[/math].

The unit circle can substitute variables for trigonometric functions.