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

Method shown in explanation

##color(blue)("This is what is happening to the graph")##

Imagine plotting the graph of ##sin(x)##. 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(x)## to the right by ##45^o##.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)("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(x-45)##

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

##color(green)("In the graph below I have shown both "color(magenta)(sin(x))" and"color(white)(,)color(blue)(sin(x-45)))## ##color(green)("so that you can see the shift to the right.")##