solving trigo without calculator

Quote:

Originally Posted by helloying

Evaluate without the use of calculator, $\sin [ \cos^{-1} (1/2) + \sin^{-1} (4/5) ]$

$\cos(\pi/3)=1/2$ (that's cos of 60 degrees, you are supposed to know this)

If $\theta=\arcsin(4/5)$ then $\sin(\theta)=4/5$ and $\cos(\theta)=3/5$ (think 3-4-5 triangle)

So new you want to know:

$\sin [ \pi/3 + \theta ]$

and you should be able to find this using the usual trig identity for the sine of a sum.

CB