Question #41349

The question tests the student's ability to derive the normal equation for a parametric curve and solve the resulting trigonometric equation while strictly adhering to domain constraints.

The 'Lethal Collision' occurs when students attempt to solve $\cos t - \sin t = 1$ by squaring both sides (yielding $\sin 2t = 0$) or by dividing by $\cos t$ (yielding $\tan t = 0$).

Squaring introduces extraneous roots (like $t = \pi/2, \pi$), leading to the trap answer $410\pi$.

Dividing by $\cos t$ loses the roots where $\cos t = 0$ (like $t = 3\pi/2$), leading to the trap answers $110\pi$ or $210\pi$.

The correct approach requires using the principal value method $R\cos(t-\alpha)$ or half-angle tangent substitution to preserve the exact solution set.