Evaluate without the use of calculator, $\displaystyle \sin [ \cos^{-1} (1/2) + \sin^{-1} (4/5) ] $
$\displaystyle \cos(\pi/3)=1/2$ (that's cos of 60 degrees, you are supposed to know this)
If $\displaystyle \theta=\arcsin(4/5)$ then $\displaystyle \sin(\theta)=4/5$ and $\displaystyle \cos(\theta)=3/5$ (think 3-4-5 triangle)
So new you want to know:
$\displaystyle \sin [ \pi/3 + \theta ] $
and you should be able to find this using the usual trig identity for the sine of a sum.
CB