What is the point of this type of graph? (Projectile) What is the point of graphing  vs range, during kinematic motion?
 A: Generally speaking, when we graph experimental data it's nice for the graph to be a straight line. This is because it's easy to tell if a graph is a straight line just by putting a ruler on it. If a graph is a curve it's hard to tell whether it's a parabola, ellipse, sine wave or some other curve without diving into some maths.
In this experiment you are varying the launch angle $\theta$ and measuring the range $R$. Let's have a look at what a graph of range against $\theta$ looks like:

This obviously isn't a straight line. So can we change the graph a bit to make it a straight line? Well, if we have a look at the Hyperphysics article on trajectories we find the range is given by the equation:
$$ R(\theta) = \frac{2v_0^2}{g}\sin\theta\cos\theta \tag{1} $$
and this obviously isn't a straight line because it's quite a complicated function. But suppose define a new variable $x$ as:
$$ x = \sin\theta\cos\theta $$
Using this new variable the equation (1) for the range becomes:
$$ R(x) = \frac{2v_0^2}{g}\, x $$
The parameters $v_0$ (the launch velocity) and $g$ (the acceleration due to gravity) are just constants, so the range is just proportional to $x$. This means a graph of the range against $x$, i.e. against $\sin\theta\cos\theta$, should be a straight line. And here's what that graph looks like:

And it is a straight line!
So that's why when you do the experiment you graph $R$ against $\sin\theta\cos\theta$. It's because the graph should be a straight line. Any deviations away from a straight line will mean either you messed up the experiment or there is some other factor that isn't included in equation (1).
In fact you may well find your graph isn't quite straight. That's because equation (1) doesn't include the effects of air resistance.
