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

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 $f \left(x\right) \to - f \left(x\right)$ 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 $f \left(x\right) \setminus \to k f \left(x\right)$ 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]}