How do you graph #y=-3/2sinx# over #0<=x<=360#?

1 Answer
May 20, 2018

See below.

Explanation:

Let's see how the function we want to study is obtain from the standard sine function, and how these transformation reflect on the graph:

  • First of all, I assume you are familiar with the graph of the standard sine function:
    graph{sin(x) [-0, 6.28, -1.5, 1.5]}
  • Then we must switch sign. The transformation #f(x) -> -f(x)# affects the graph by vertical symmetry (we reflect with respect to the #x# axis:
    graph{-sin(x) [-0, 6.28, -1.5, 1.5]}
  • Finally, we multiply the function by a constant: the transformation #f(x) \to kf(x)# results in a vertical stretch if #k>1#, or a vertical compression otherwise. In our case, we're stretching the graph by a factor #1.5#. Note how the new maximum and minimum is not #1# anymore but #1.5#
    standard sine function:
    graph{-1.5*sin(x) [-0, 6.28, -2, 2]}