Question

Упростить выражение:
3cos(7/4пи)+2sin(3/4пи)-sin(-9/4пи)+7cos(13/2пи)

Answer 1

$3cosfrac{7pi}{4}+2sinfrac{3pi}{4}-sin(-frac{9pi}{4})+7cosfrac{13pi}{2}=3cos(pi+frac{3pi}{4})+2sin(frac{pi}{2}+frac{pi}{4})\+sin(2pi+frac{pi}{4})+7cos(6pi+frac{pi}{2})=-3cosfrac{3pi}{4}+2cosfrac{pi}{4}+sinfrac{pi}{4}+7cosfrac{pi}{2}=\=-3cos(frac{pi}{2}+frac{pi}{4})+2cosfrac{pi}{4}+sinfrac{pi}{4}+7cosfrac{pi}{2}=3sinfrac{pi}{4}+2cosfrac{pi}{4}+sinfrac{pi}{4}+\+7cosfrac{pi}{2}=4sinfrac{pi}{4}+2cosfrac{pi}{4}+7cosfrac{pi}{2}=$
$=4*frac{sqrt2}{2}+2*frac{sqrt2}{2}+7*0=3sqrt2$