Show That the Curve with Vector Equation R (T) = $\cos ^ { 2 } t$

Essay

Show that the curve with vector equation r (t) = 2 $\cos ^ { 2 } t$ i + sin (2t) j + 2 sin t k is the curve of intersection of the surfaces $( x - 1 ) ^ { 2 } + y ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ Use this fact to sketch the curve.