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

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- Jun 27th 2009, 12:45 AMhelloyingsolving trigo without calculator
Evaluate without the use of calculator, $\displaystyle \sin [ \cos^{-1} (1/2) + \sin^{-1} (4/5) ] $

- Jun 27th 2009, 01:39 AMCaptainBlack
$\displaystyle \cos(\pi/3)=1/2$ (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