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
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)}
