# How do you graph  y=-2+sin(2x+pi)?

Dec 2, 2016

Please see the explanation.

#### Explanation:

The -2 shifts the graph down 2 units, therefore, the graph will vary from -1 to -3.

The 2 multiplying the x makes the graph repeat 2 twice as fast as the normal sine function. Another way of saying this is, it changes the period from $2 \pi$ to $\pi$.

The 2 multiplier, also, changes the phase shift; you divide the $\pi$ that is add by the 2 multiplier and change the sign to find that the phase shift is $- \frac{\pi}{2}$. This means that you will find the zero crossing that normally starts a sine curve to the left of the y axis by $\frac{\pi}{2}$.

Here is a graph of the function.