Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 602: 2

At $t=0$, the coordinate is $(1,0)$. At $t=\pi/4$, the coordinate is $(0,1/2)$. At $t=\pi$, the coordinate is $(1,0)$.

At $t=0$, then $x=\cos 2t=\cos 0=1$ and $y=\sin^2t=\sin^20$. The coordinate is $(1,0)$. At $t=\pi/4$, then $x=\cos 2t=\cos \pi/2=0$ and $y=\sin^2t=\sin^2\pi/4=1/2$. The coordinate is $(0,1/2)$. At $t=\pi$, then $x=\cos 2t=\cos 2\pi=1$ and $y=\sin^2t=\sin^2\pi=0$. The coordinate is $(1,0)$.