Question

Решить Уравнение

1)sin(x/3 - пи/4)=-12
2)cos 4x = √32

Answer 1

1)

$displaystyle sin(frac{x}{3}-frac{pi}{4})= -frac{1}{2}\\ left[begin{array}{ccc}frac{x}{3}-frac {pi}{4}=-frac{pi}{6}+2pi n; nin Z \ frac{x}{3}-frac{pi }{4} =-frac{5pi }{6}+2pi n; nin Z\ end{array}$

$left[begin{array}{ccc}frac{x}{3}=+frac {pi}{4}-frac{pi}{6}+2pi n; nin Z \ frac{x}{3}=+frac{pi }{4}-frac{5pi }{6}+2pi n; nin Z\end{array}$

$left[begin{array}{ccc}frac{x}{3}=frac{pi}{12}+2pi n; nin Z \frac{x}{3}=-frac{7pi }{12}+2pi n; nin Z\end{array}$

$left[begin{array}{ccc}x=frac{pi}{4}+6pi n; nin Z \x =-frac{7pi }{4}+6pi n; nin Z\ end{array}$

2)

$displaystyle cos(4x)=frac{sqrt{3}}{2}\\4x= pm frac{pi }{6} +2pi n; nin Z\\ x=pmfrac{pi}{24}+frac{pi n}{2} ; nin Z$