Answer to Question #252507 in Calculus for Kenneth Pondang

Question

If g(x)=cos 2x. Find g(\pi /4), g(\pi /2), g(\pi -x), g(\pi +x), g(x-\pi /2)

Answer 1

$g(x)=cos(2x)$

$\therefore g(\frac{\pi}{4})=cos(\frac{\pi}{2})=0\\ g(\frac{\pi}{2})=cos(\pi)=-1\\ g(\pi-x)=cos(2(\pi-x))=cos(2\pi-2x)=cos2x\\ g(\pi+x)=cos(2(\pi+x))=cos(2\pi+2x)=cos2x\\ g(x-\frac{\pi}{2})=cos(2(x-\frac{\pi}{2}))=cos(2x-\pi)=cos(\pi-2x)=-cos2x$