PLEASE HELP (100 POINTS)

Question

asked Jun 9, 2023 105k views

2 Answers

Ilian Iliev · Answer 1 · 2023-06-13T12:39:13+0000

$\\ \rm\Rrightarrow f(x)=-5cos(x)/(2)+5$

Compare to standard equation of SHM

$\\ \rm\Rrightarrow y=Acos(\omega x+\phi)$

Here

$\\ \rm\Rrightarrow \omega x=(x)/(2)$

$\\ \rm\Rrightarrow \omega=1/2$

Well the above one are for extra knowledge .

Solution:-

$\\ \rm\Rrightarrow 10=-5cos(x)/(2)+5$

$\\ \rm\Rrightarrow 10-5=-5cos(x)/(2)$

$\\ \rm\Rrightarrow 5=-5cos(x)/(2)$

$\\ \rm\Rrightarrow cos(x)/(2)=-1$

$\\ \rm\Rrightarrow (x)/(2)=cos^(-1)(-1)$

$\\ \rm\Rrightarrow (x)/(2)=\pi$

$\\ \rm\Rrightarrow x=2\pi$

So.

$\\ \rm\Rrightarrow x=2\pi+2\pi n$