# How do I find the value of sin 225?

Oct 29, 2015

$- \frac{1}{\sqrt{2}}$

#### Explanation:

$\sin {225}^{\circ} = \sin \left({180}^{\circ} + {45}^{\circ}\right)$

$= \sin {180}^{\circ} \cos {45}^{\circ} + \cos {180}^{\circ} \sin {45}^{\circ}$

$= \left(0\right) \left(\frac{1}{\sqrt{2}}\right) + \left(- 1\right) \frac{1}{\sqrt{2}}$

=$- \frac{1}{\sqrt{2}}$