Question

What does the graph of `f(x) = (sin^3x + sinxcos^2x)/sinx` look like?

Answer 1

We start by noticing that for it to be defined, the function cannot have `sinx = 0`, aka `x != 2pin` or `pi + 2pin`. Now we notice

`f(x) = (sinx(sin^2x+ cos^2x))/sinx`

`f(x) = sin^2x + cos^2x`

`f(x) = 1`

So the graph of the function will be the line `y = 1`, but with holes at `x = 2pin` or `x = pi + 2pin`, where `n` is an integer.

Hopefully this helps!