How do you graph y = sin (x + 30°)?

1 Answer
Jul 10, 2016

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]}