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?

Find a sine and cosine function for the graph below

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

1 Answer 1


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


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