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

1 Answer
Douglas K.
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 #2pi# 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 #-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 #pi/2#.

Here is a graph of the function.
enter image source here

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