Answer
$3\cos x$
Work Step by Step
Given that graph is of trigonometric function and starts with maxima
Using general equation $y = k + A\cos (Bx + C)$
We know that
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Vertical\ shift = k$
Period is $2\pi$ this gives B = 1
Amplitude is 3 so $A=3$
No vertical shift found as average of maximum and minimum is 0
so k = 0
The graph has
y = 3 at $x = 0, 2\pi$
y = 0, at x = $\frac{\pi}{2}$
So it clearly is graph of $3\cos x$
