Online Math Tutor LLC

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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. 

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