Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Angles

Unit Circle

Unit Circle Related Diagrams

Location \(\theta\) \(\texttt{sin}(\theta)\) \(\texttt{cos}(\theta)\) \(\texttt{tan}(\theta)\)
x-axis \(0\) \(0\) \(1\) \(0\)
Quadrant 1  \(\displaystyle\frac{\pi}{6}\) \(\displaystyle\frac{1}{2}\) \(\displaystyle\frac{\sqrt{3}}{2}\) \(\displaystyle\frac{\sqrt{3}}{3}\)
\(\displaystyle\frac{\pi}{4}\) \(\displaystyle\frac{\sqrt{2}}{2}\) \(\displaystyle\frac{\sqrt{2}}{2}\) \(\displaystyle 1\)
\(\displaystyle\frac{\pi}{3}\) \(\displaystyle\frac{\sqrt{3}}{2}\) \(\displaystyle\frac{1}{2}\) \(\displaystyle\sqrt{3}\)
y-axis \(\displaystyle\frac{\pi}{2}\) \(1\) \(0\) \(\texttt{DNE}\)
Location \(\theta\) \(\texttt{sin}(\theta)\) \(\texttt{cos}(\theta)\) \(\texttt{tan}(\theta)\)
y-axis \(\displaystyle\frac{\pi}{2}\) \(1\) \(0\) \(\texttt{DNE}\)
Quadrant 2   \(\displaystyle\frac{\pi}{3}\) \(\displaystyle\frac{\sqrt{3}}{2}\) \(\displaystyle-\frac{1}{2}\) \(\displaystyle-\sqrt{3}\)
\(\displaystyle\frac{\pi}{4}\) \(\displaystyle\frac{\sqrt{2}}{2}\) \(\displaystyle-\frac{\sqrt{2}}{2}\) \(\displaystyle-1\)
\(\displaystyle\frac{\pi}{6}\) \(\displaystyle\frac{1}{2}\) \(\displaystyle-\frac{\sqrt{3}}{2}\) \(\displaystyle-\frac{\sqrt{3}}{3}\)
x-axis \(\pi\) \(0\) \(1\) \(0\)
Location \(\theta\) \(\texttt{sin}(\theta)\) \(\texttt{cos}(\theta)\) \(\texttt{tan}(\theta)\)
x-axis \(\pi\) \(0\) \(-1\) \(0\)
Quadrant 3 \(\displaystyle\frac{7\pi}{6}\) \(\displaystyle\frac{1}{2}\) \(\displaystyle-\frac{\sqrt{3}}{2}\) \(\displaystyle\frac{\sqrt{3}}{3}\)
\(\displaystyle\frac{5\pi}{4}\) \(\displaystyle-\frac{\sqrt{2}}{2}\) \(\displaystyle-\frac{\sqrt{2}}{2}\) \(\displaystyle 1\)
\(\displaystyle\frac{4\pi}{3}\) \(\displaystyle-\frac{\sqrt{3}}{2}\) \(\displaystyle-\frac{1}{2}\) \(\displaystyle\sqrt{3}\)
y-axis \(\displaystyle\frac{3\pi}{2}\) \(-1\) \(0\) \(\texttt{DNE}\)
Location \(\theta\) \(\texttt{sin}(\theta)\) \(\texttt{cos}(\theta)\) \(\texttt{tan}(\theta)\)
y-axis \(\displaystyle\frac{3\pi}{2}\) \(-1\) \(0\) \(\texttt{DNE}\)
Quadrant 4 \(\displaystyle\frac{5\pi}{3}\) \(\displaystyle-\frac{\sqrt{3}}{2}\) \(\displaystyle\frac{1}{2}\) \(\displaystyle-\sqrt{3}\)
\(\displaystyle\frac{7\pi}{4}\) \(\displaystyle-\frac{\sqrt{2}}{2}\) \(\displaystyle\frac{\sqrt{2}}{2}\) \(\displaystyle -1\)
\(\displaystyle\frac{11\pi}{6}\) \(\displaystyle-\frac{1}{2}\) \(\displaystyle\frac{\sqrt{3}}{2}\) \(\displaystyle-\frac{\sqrt{3}}{3}\)
x-axis \(\displaystyle2\pi\) \(0\) \(1\) \(0\)

*Be sure to take some time to memorize these special angle values on the unit circle.