In reading many tutorials on parametric equations, there is always a step that appears to be magic to me.
Take, for example, the parametric equation of x = sin(t), y = cos(t), 0 <= t <= pi.
To eliminate t, it is always referenced that x^2 + y^2 = 1, and so this is the final result. But that seems to be completely missing any steps.
I don't understand how the jump from question to result has occurred, and why that train of thought is taken. My intuition would just be to say t is arcsin(x), which makes for the messy equation of y = cos(arcsin(x)).