Chapter 17.7, Problem 2QC

In Example 3a We used the parameterization r(t) = $\langle \cos t,\sin t,3{\cos }^{2}t+{\sin }^{2}t\rangle$for C. Confirm that the parameterization C : r(t) = $\langle \cos t,\sin t,4-co{s}^{2}t-3{\sin }^{2}t\rangle$ also results in an answer of $2\pi$.