# How do you determine sin 345?

Apr 21, 2018

See solution details below

#### Explanation:

we know that $345 = 300 + 45$

Now let use the formula

$\sin \left(a + b\right) = \sin a \cos b + \sin b \cos a$ in our case

$\sin \left(300 + 45\right) = \sin 300 \cos 45 + \sin 45 \cos 300$

But $\sin 300 = - \sin 60 = - \frac{\sqrt{3}}{2}$ and $\cos 300 = \cos 60 = \frac{1}{2}$ and $\sin 45 = \cos 45 = \frac{\sqrt{2}}{2}$

Lets go to prior formula

$\sin 345 = \sin \left(300 + 45\right) =$
=-sqrt3/2·sqrt2/2+sqrt2/2·1/2=sqrt2/4-sqrt6/4=1/4(sqrt2-sqrt6)