I know how to parametrize a function but the motivation of how to pick any particular way is confusing me. This example will help me out.
Start with a simple parabola y = x^2 in rectangular coordinates. And let x = sin (t) . Now the y rectangular coordinate is y = (sin(t))^2.
The orientation must make a difference of course if it is truly parametrized . The only functional difference should be the speed ? How would that affect our rectangular function in this case and what does the graph look like? This should clear my confusion. Thank you .