# How do I find the value of sin 105?

It is $\sin {105}^{o} = \frac{1}{4} \cdot \left(\sqrt{6} + \sqrt{2}\right)$

#### Explanation:

We have that

$\sin \left(105\right) = \sin \left(60 + 45\right)$

because

$\sin \left(a + b\right) = \sin a \cdot \cos b + \cos a \cdot \sin b$

hence, we have

sin105=sin(60+45)=sin60*cos45+cos60*sin45= =sqrt3/2*sqrt2/2+1/2*sqrt2/2=1/4(sqrt6+sqrt2)