Question

Зная что cosa = - 35, П2 <a <П, найдите sin (  ( П4 ) + a)

Answer 1

$sina= sqrt{1-cos^{2}a}\sina= sqrt{1-(- frac{3}{5})^{2}}=sqrt{1- frac{9}{25}}= sqrt{frac{16}{25}}= frac{4}{5} \ sin( frac{ pi }{4}+a)=sin frac{ pi }{4}cosa+cos frac{ pi }{4}sina;\ frac{ sqrt{2}}{2}*(- frac{3}{5})+ frac{ sqrt{2}}{2}* frac{4}{5}=- frac{3 sqrt{2}}{10}+ frac{4 sqrt{2}}{10}= frac{ sqrt{2}}{10}$

Answer 2

$sin alpha = sqrt{1- cos alpha ^{2} } = sqrt{1- frac{9}{25} } = frac{4}{5} =0.8$
$sin( pi /4+ alpha ) =sin( pi /4)cos( alpha )+cos( pi /4)sin( alpha )$
$frac{ sqrt{2} }{2}*(- 0.6)+frac{ sqrt{2} }{2}*0.8=frac{ sqrt{2} }{2}*0.2=frac{ sqrt{2} }{2}* frac{1}{5}$

Answer 3

$sin alpha = sqrt{1- cos alpha ^{2} } = sqrt{1- frac{9}{25} } = frac{4}{5} =0.8$
$sin( pi /4+ alpha ) =sin( pi /4)cos( alpha )+cos( pi /4)sin( alpha )$
$frac{ sqrt{2} }{2}*(- 0.6)+frac{ sqrt{2} }{2}*0.8=frac{ sqrt{2} }{2}*0.2=frac{ sqrt{2} }{2}* frac{1}{5}=frac{ sqrt{2} }{10}$