Question

How do you graph `y = sin (x + 30°)`?

Answer 1

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]}