How do you graph y=2+sin(1/2x)?

1 Answer
Aug 14, 2017

Draw a sine wave with twice the wavelength. Then shift it UP two units.

Explanation:

You know what the graph of sin(x) is.

  • when x is 0, y = 0
  • when x is pi/2, y=1
  • when x is pi, y=0
  • when x is (3*pi)/2, y=-1
  • when x is 2*pi, y=0

graph{sin(x) [-10, 10, -5, 5]}

So now, for y = sin(x/2):

  • when x is 0, x/2 is 0 , y= 0
  • when x is pi, x/2 is pi/2, y= 1
  • when x is 2 * pi, x/2 is pi , y= 0
  • when x is 3 * pi, x/2 is (3*pi)/2 , y= -1
  • when x is 4 * pi, x/2 is 2 * pi , y= 0

So, it's the same sine wave, but stretched out.

Now, since your function is 2 + sin(x/2), simply add 2 to the value for y in the table above:

  • when x is 0, y= 2
  • when x is pi, y= 3
  • when x is 2 * pi, y= 2
  • when x is 3 * pi, y= 1
  • when x is 4 * pi , y= 2

graph{2 + sin(x/2) [-10, 10, -5, 5]}