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Unit circle facts for kids

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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 x^2 + y^2 = 1. 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 t is the angle desired, x and y can be defined as \cos (t) = x and \sin (t) = y. Using the function of the unit circle, x^2 + y^2 = 1, another equation for the unit circle is found, \cos^2(t) + \sin^2(t) = 1. When working with trigonometric functions, it is mainly useful to use angles with measures between 0 and \pi\over 2 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: \cos (t)  = \cos (2 \cdot \pi k + t) and sin (t) = \sin (2 \cdot \pi k + t) for any integer k.

Unit circle
The unit circle can substitute variables for trigonometric functions.

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