Question

SOS! SOS! SOS!

cos(3x+pi/2)=✓2/2

Answer 1

$Cos(3x+\frac{\pi }{2})=\frac{\sqrt{2} }{2}\\\\-Sin3x=\frac{\sqrt{2} }{2}\\\\Sin3x=-\frac{\sqrt{2} }{2}\\\\3x=(-1)^{n}arcSin(-\frac{\sqrt{2} }{2})+\pi n,n\in Z\\\\3x=(-1)^{n+1}\frac{\pi }{4}+\pi n,n\in Z\\\\\boxed{x=(-1)^{n+1}\frac{\pi }{12}+\frac{\pi n }{3},n\in Z}$