How do you graph #y = sin (x + 30°)#?

1 Answer
Jul 10, 2016

Answer:

The graph is the same as for #y = sin(x)# but with the phase shifted to the left by #30°#.

Explanation:

Because we are adding 30 degrees (which is equivalent to #pi/6#) to the function #sin(x)#, the result will be a shift of the whole function to the left. This is true for any function, adding a constant to a variable shifts the function in the direction of that variable by the inverse of the constant added.

This can be observed here:

Graph of #sin(x)#
graph{sin(x) [-10, 10, -5, 5]}

Graph of #sin(x + pi/6)#
graph{sin(x+pi/6) [-10, 10, -5, 5]}