Chapter 6.7, Problem 369E

For the following exercises, let $S$ he the disk enclosed by curve $C:\text{r}(t)=\langle \cos \phi \cos t,\sin t\sin \phi \cos t\rangle$ , for $0\le t\le 2\pi$ , where $0\le \phi \le \frac{\pi }{2}$ is a fixed angle.

369. What is the circulation of $C$ of vector field as $\text{F}=\langle -y-z,x\rangle$ a function of $\phi$ ?