Question

Вычислите:
1. cos 5П/3
2. sin345°
3. tg(-240°)

Answer 1

$1.; cosfrac{5pi}{3}=cos(frac{6pi}{3}-frac{pi}{3})=cos(2pi-frac{pi}{3})=cosfrac{pi}{3}=frac{1}{2};\\ 2. ; sin345^o=sin(360^o-15^o)=-sin15^o=-sin(45^o-30^o)=\=-(sin45^ocos30^o-cos45^osin30^o)=-(frac{sqrt2}{2}*frac{sqrt3}{2}-frac{1}{2}*frac{1}{2})=frac{1-sqrt6}{4};\\ 3.; tg(-240^o)=-tg(270^o-30^o)=-tg30^o=-frac{sqrt3}{3}.$