# Find a sine function for this graph

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?

• this graph is $2\sin(\frac{1}{2}(x-\pi /2))-2$ Sep 19, 2015 at 18:32
• So your period and phase shift is wrong. Sep 19, 2015 at 18:36
• its period is $4\pi$ is easy to observe Sep 19, 2015 at 18:50

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