# Math Help - Exact Value of the expression without a calculator

1. ## Exact Value of the expression without a calculator

sin(3pi/12)cos(pi/12)+cos(3pi/4)sin(pi/12)

I tried it like this sqrt2/2 (sqrt2/4+sqrt6/4)+(-sqrt2/2+?
I'm not sure if how to approach it

2. ## Re: Exact Value of the expression without a calculator

Originally Posted by LAPOSH42
sin(3pi/12)cos(pi/12)+cos(3pi/4)sin(pi/12)
$\sin(\theta)\cos(\phi)+\cos(\theta)\sin(\phi)=\sin (\theta+\phi)
$

And $~\frac{4\pi}{12}=\frac{\pi}{3}$

3. ## Re: Exact Value of the expression without a calculator

sin(3pi/12) = sin(pi/4) and cos(3pi/4) = -cos(pi/4) so your expression becomes

sin(pi/4)cos(pi/12) - cos(pi/4)sin(pi/12) = sin[(pi/4) - (pi/12)] => sin(pi/6)