What is the graph of ##y=sin(x+30)##?

The graph ##y=sin(x+30)## looks like that of a regular sin graph except it is shifted left by 30 degrees.

Explanation:

Remember, that when you add or subtract from the angle in a sin graph (the variable), it shifts the graph left or right.

Adding to the variable shifts the graph left, subtracting shifts the graph right.

The red line is a regular sin, and the blue line is sin (x+30):

To shift the whole graph up or down, you’d add a number to the whole equation, like this: ##y=sin(x)+2##

Remember that you need to know if the asker is dealing with degrees or radians. For this example I assumed we were dealing in degrees.