The following table shows a selection of frequently used angles and the associated results of the trigonometric functions sine and cosine.
\[ \require{cancel} \]| \[ [\alpha]=rad \] | \[ [\alpha]=° \] | \[ \sin \alpha \] | \[ \cos \alpha \] |
| \[ 0 \] | \[ 0° \] | \[ 0 \] | \[ 1 \] |
| \[ \frac{\pi}{6} \] | \[ 30° \] | \[ \frac{1}{2} \] | \[ \frac{\sqrt{3}}{2} \] |
| \[ \frac{\pi}{4} \] | \[ 45° \] | \[ \frac{1}{\sqrt{2}} \] | \[ \frac{1}{\sqrt{2}} \] |
| \[ \frac{\pi}{3} \] | \[ 60° \] | \[ \frac{\sqrt{3}}{2} \] | \[ \frac{1}{2} \] |
| \[ \frac{\pi}{2} \] | \[ 90° \] | \[ 1 \] | \[ 0 \] |
| \[ \frac{2\pi}{3} \] | \[ 120° \] | \[ \frac{\sqrt{3}}{2} \] | \[ -\frac{1}{2} \] |
| \[ \frac{3\pi}{4} \] | \[ 135° \] | \[ \frac{1}{\sqrt{2}} \] | \[ -\frac{1}{\sqrt{2}} \] |
| \[ \frac{5\pi}{6} \] | \[ 150° \] | \[ \frac{1}{2} \] | \[ -\frac{\sqrt{3}}{2} \] |
| \[ \pi \] | \[ 180° \] | \[ 0 \] | \[ -1 \] |
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 (°)
\[ \alpha_{Degree} = \frac{\alpha_{Radiant}}{\pi} \cdot 180° \]
