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

1 Answer
Feb 28, 2016

Method shown in explanation

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.

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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:

Tony B

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.")

Tony B