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I have a curve $ y = a sin( b(x + c) )+ d $, the sketch looks likes this

I'm able to calculate value of $a=\frac{max-min}{2}=1.5$, $d=2$ and $b=\pi$.

I need help solving $c$, I know it gives a horizontal shift to the function and can be solved now by forming an equation, my question is how can we solve it from the graph ? (how to identify horizontal shift, and hence find $c.$

Any help is appreciated.

Thank you, Arif

1 Answers 1

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It looks like $c=-\frac{1}{2}+ 2n$ with $n \in \mathbb Z$.

You may for example observe that the minimum of $y$ is attained for $x=0$, and the min of $\sin(t)$ is attained for $t=-\frac{\pi}{2}+2n\pi$

So $\pi c=-\frac{\pi}{2}+2n\pi$ from where you can get $c=-\frac{1}{2}+2n$

You may take either $c=-\frac{1}{2}$ or $c=\frac{3}{2}$ (if you want it positive)

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    yes the smallest positive value of $c=1.5$ , any links to learn more such examples would help a lot. – 2017-01-09
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    I found $d=\frac{max+min}{2}$ is that the correct method ?, PS any resources that could help me solve more such problems will be of great help. – 2017-01-09
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    Yes, it is correct. You may try some youtube videos, for example [this](https://www.youtube.com/watch?v=bvTR9XbL1co). So you see that an easier way to calculate the phase shift is to look for the point where your $\sin$ is increasing and intersects the vertical shift (which in your case is $1/2$). Then your $c$ is the opposite $c=-1/2$ – 2017-01-09