Parametric Equations

Curves with a parameter

Eliminating the parameter

The cycloid

Motion along curves

What can parametric equations describe that a single function y = f(x) cannot?

The parametric equations x = t - 1, y = 2t + 4 eliminate to which ordinary equation?

The parametrization x = a cos t, y = b sin t traces which curve?

The cycloid x = r(t - sin t), y = r(1 - cos t) touches the ground with sharp corners called cusps. Where do they occur?

The parametrization x = cos(2t), y = sin(2t) on the interval [0, 2 pi) traces the unit circle how?

The line x = 1 + 2t, y = 3 - t has direction vector (2, -1). As a number, what is its x component? Answer with a number.

The unit circle x = cos t, y = sin t at t = 0 sits at which x coordinate? Answer with a number.

The cycloid's arches rise to height 2r. As a multiple of r, what is the maximum y? Answer with a number.

The projectile path x = v0 cos(theta) t, y = v0 sin(theta) t - 4.9 t^2 has which parameter?

Reversing the parameter, t to -t, reverses the curve's orientation. As one word, what is preserved? Answer in lowercase.