Answer
$–2 \sin x$
Work Step by Step
The graph is the inverted graph of problem 12
which implies it is $–2 \sin x$
or by using deduction
since graph is inverted and starts with $y = 0$
Using general equation $y = k – A\sin (Bx + C)$
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Vertical\ shift = k$
Period is $2\pi$ this gives B = 1
Amplitude is 2 so $A=2$
No vertical shift found as average of maximum and minimum is 0
so k = 0
The graph has
y = 0 at $x = 0, 2\pi $
y = -1, at x = $\frac{\pi}{2}$
y =1 at $x = \frac{3\pi}{2}$
As graph starts with y = 0, at x = 0
Horizontal shift = 0, => C =0
this gives graph as $–2 \sin x$
