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# Important angles and related results of the trigonometric functions

The following table shows a selection of frequently used angles and the associated results of the trigonometric functions sine and cosine.

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 $[\alpha]=rad$ $[\alpha]=°$ $\sin \alpha$ $\cos \alpha$ $0$ $0°$ $0$ $1$ $\frac{\pi}{6}$ $30°$ $\frac{1}{2}$ $\frac{\sqrt{3}}{2}$ $\frac{\pi}{4}$ $45°$ $\frac{1}{\sqrt{2}}$ $\frac{1}{\sqrt{2}}$ $\frac{\pi}{3}$ $60°$ $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $\frac{\pi}{2}$ $90°$ $1$ $0$ $\frac{2\pi}{3}$ $120°$ $\frac{\sqrt{3}}{2}$ $-\frac{1}{2}$ $\frac{3\pi}{4}$ $135°$ $\frac{1}{\sqrt{2}}$ $-\frac{1}{\sqrt{2}}$ $\frac{5\pi}{6}$ $150°$ $\frac{1}{2}$ $-\frac{\sqrt{3}}{2}$ $\pi$ $180°$ $0$ $-1$

The shown values are typically used for simplified notation of mechanical equations. In addition, the table can be used for the conversion between ° and radiant.

Angle conversion from Degree (°) to Radiant

$\alpha_{Radiant} = \frac{\alpha_{Degree}}{180°} \cdot \pi$

Angle conversion from Radiant to Degree (°)

$\alpha_{Degree} = \frac{\alpha_{Radiant}}{\pi} \cdot 180°$