# How do you graph y = sin (x + 30°)?

Jul 10, 2016

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

#### Explanation:

Because we are adding 30 degrees (which is equivalent to $\frac{\pi}{6}$) to the function $\sin \left(x\right)$, 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 $\sin \left(x\right)$
graph{sin(x) [-10, 10, -5, 5]}

Graph of $\sin \left(x + \frac{\pi}{6}\right)$
graph{sin(x+pi/6) [-10, 10, -5, 5]}