The equations … and … also lead to …—but they are different…

The equations $x={\cos }^2\theta$ and $y={\sin }^2\theta$ also lead to $x+y=1$—but they are different from the answer to Problem 29. Explanation: $\theta$ is no longer the polar angle and we should have written $t$. Find a point $x={\cos }^2\theta ,y={\sin }^2\theta$ that is _not_ at the angle $\theta$.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §9.1 Polar Coordinates, #30