Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator? 
Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator?
$150$ degree 

the right answer are $\frac{1}{2}$, $-\frac{\sqrt{3}}{2}$and $-\frac{1}{\sqrt{3}} $

$-315$ degree

the right answer are $\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$ and $1$.

It is very simple.  
$\sin(150) = \sin(90+60) = \cos(60)  = \frac{1}{2}$
$\cos(150) = \cos(90+60) = - \sin(60) = -\frac{\sqrt{3}}{2}$
$\tan(150) = \tan(90+60) = - \cot(60) = -\frac{1}{\sqrt{3}} $
similarly 
$\sin(-315)=-\sin(270+45)=\cos(45) = \frac{1}{\sqrt{2}}$
$\cos(-315)=\cos(315)=\cos(270+45)=\sin(45)  = \frac{1}{\sqrt{2}}$
$\tan(-315)=-\tan(270+45)=\cot(45) = 1$
Check this link for more info on converting trigo identities
