Question

Find the equations of the tangent lines at the point where the curve crosses itself. (enter your answers as a comma-separated list of equations.) x = 2 − π cos t y = 2t − π sin t −π ≤ t < π

Answer 1

A graph shows the curve crosses itself at (x, y) = (2, 0). It has those coordinates for t = ±π/2. The slope (m) of the curve is the ratio
  m = (dy/dt)/(dx/dt)
  m = (2 -π·cos(t))/(π·sin(t))
At t = -π/2, this is
  m = (2 - 0)/(-π) = -2/π
At t = π/2, this is
  m = (2 - 0)/(π) = 2/π

In point-slope form the equations of the tangent lines are
  {y = (-2/π)(x -2), y = (2/π)(x -2)}