#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#.

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#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.")#