Unit circle

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 $k$.

The unit circle can substitute variables for trigonometric functions.