Question

Show that the curve with parametric equations x = t cos t, y = t sin t, z = t lies on the cone z2 = x2 + y2.

Answer 1

`x^2 + y^2 = (t\cos(t))^2 + (t\sin(t))^2 \\\\ ~~~~~~~~~~~ = t^2 \cos^2(t) + t^2 \sin^2(t) \\\\ ~~~~~~~~~~~ = t^2 \bigg(\cos^2(t) + \sin^2(t)\bigg) \\\\ ~~~~~~~~~~~= t^2 \\\\ ~~~~~~~~~~~ = z^2`