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.