Question

Cos(π(2x+9)/3)=½
tg(π(x-5)/3)= -√3
sin(πx/3)=0,5

Answer 1

$1); ; cosfrac{pi (2x+9)}{3} = frac{1}{2} \\ frac{pi (2x+9)}{3} =pm frac{pi}{3}+2pi n,; nin Z\\2x+9=pm 1+6n; ,; nin Z\\2x=pm 1-9+6n; ,; nin Z\\x=pm 0,5-4,5+3n; ,; nin Z\\2); ; tgfrac{pi (x-5)}{3}=-sqrt3\\frac{pi(x-5)}{3}=-frac{pi}{3}+pi n,; nin Z\\x-5=-1+3n; ,; nin Z\\x=4+3n; ,; nin Z$

$3); ; sinfrac{pi x}{3}=0,5\\frac{pi x}{3}=(-1)^{n}frac{pi}{6}+pi n,; nin Z\\x=(-1)^{n}cdot frac{1}{2}+3n; ,; nin Z$