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 $\frac{\pi }{2}$ 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.