Question

Помогите решить простейшие триг. ур

1) 10sin4x=4
2)5 sin x/4=-3
3) 8cos4x+7=0
4) 5cos pi/2-4=0​

Answer 1

$1)10sin(4x)=4<=>sin(4x)=\frac{2}{5}<=>4x=(-1)^karcsin(\frac{2}{5})+\pi k<=>\\<=>x=\frac{(-1)^karcsin(\frac{2}{5})+\pi k}{4} \\2)5sin(\frac{x}{4} )=-3<=>sin(\frac{x}{4})=-\frac{3}{5}<=>\frac{x}{4}=(-1)^{k+1}arcsin(\frac{3}{5} )+\pi k<=>\\<=>x=4(-1)^{k+1}arcsin(\frac{3}{5} )+4\pi k$

$3)8cos(4x)+7=0<=>cos(4x)=-\frac{7}{8}<=>4x=\pi+-arccos(\frac{7}{8} )+2\pi k<=>\\<=>x=\frac{\pi+-arccos(\frac{7}{8} )}{4} +\frac{\pi k}{2}\\ 4) 5cos(\frac{\pi}{2} )-4=0-4=-4$