# How do you graph  y = sin(x - 45)?

Feb 28, 2016

Method shown in explanation

#### Explanation:

$\textcolor{b l u e}{\text{This is what is happening to the graph}}$

Imagine plotting the graph of $\sin \left(x\right)$. Pick any value for $x$. Move along the x-axis to the left by ${45}^{o}$. Note the y-value at that point. Now go back to your original x-value and mark a point at the y-value you just made not of,

In other words you are moving the graph of $\sin \left(x\right)$ to the right by ${45}^{o}$.

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$\textcolor{b l u e}{\text{Method}}$
Build a table of values choosing values for $x$ that you think are appropriate. It should look something like this:

You then put small crosses or dots on the graph paper that match the values for y and $\sin \left(x - 45\right)$

As best as you can draw a smooth free hand curve that connects the points/crosses.

$\textcolor{g r e e n}{\text{In the graph below I have shown both "color(magenta)(sin(x))" and} \textcolor{w h i t e}{,} \textcolor{b l u e}{\sin \left(x - 45\right)}}$ $\textcolor{g r e e n}{\text{so that you can see the shift to the right.}}$