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

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Answer 1 · 2018-05-20T11:28:01

See below.

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]}