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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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