# Question #19c60

Nov 8, 2014

$\sin \left({330}^{\circ}\right) + \cos \left({315}^{\circ}\right) + \tan \left({45}^{\circ}\right)$

by subtracting ${360}^{\circ}$ from the first two angles,

$= \sin \left(- {30}^{\circ}\right) + \cos \left(- {45}^{\circ}\right) + \tan \left({45}^{\circ}\right)$

since sine is an odd function, and cosine is an even function,

$= - \sin \left({30}^{\circ}\right) + \cos \left({45}^{\circ}\right) + \tan \left({45}^{\circ}\right)$

by using special triangles,

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

I hope that this was helpful.