Question

2sin(p/3-x/4)=√3/2 решить уравнение

Answer 1

$2sin( frac{pi}{3} - frac{x}{4} )= frac{sqrt{3}}{2} \sin( frac{pi}{3} - frac{x}{4} )= frac{sqrt{3}}{4} \ frac{pi}{3} - frac{x}{4}=arcsin( frac{sqrt{3}}{4})+2pi n, n in Z\frac{x}{4}=frac{pi}{3}-arcsin( frac{sqrt{3}}{4})-2pi n, n in Z\x_1= frac{4pi}{3} -4arcsin( frac{sqrt{3}}{4})-8pi n, n in Z\frac{pi}{3} - frac{x}{4}=pi-arcsin( frac{sqrt{3}}{4})+2pi n, n in Z\ frac{x}{4}= frac{pi}{3} -pi+arcsin( frac{sqrt{3}}{4})-2pi n, n in Z\x_2=- frac{8pi}{3} +4arcsin( frac{sqrt{3}}{4})-8pi n, n in Z$