Find a sine function for this graph

Question

I'm trying to find the equation for this graph, and my answer was:

Amplitude: $2$
Period: $1$ because $\pi/2 + 3\pi/2 = 2\pi$
Phase Shift: $-\pi/2$
Vertical shift: $-2$

So my answer is: $$2\sin(x + \pi/2) - 2$$ The problem is that when I enter this equation in Desmos Graphing Calcultor to make sure that my answer is right, I get similar graph but not the same one in my booklet

So what's wrong with my equation?

Answer 1

Booklet plot is a plot of $ 2 (\sin(x /2 - \pi/4) - 1),\, -2 \pi <x <2 \pi. $