Question

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

Answer 1

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]}