Chapter 12.3, Problem 39ES

Find a change of parameter $t=g\left(\tau \right)$ for the semicircle $\text{r}\left(t\right)=\cos t\text{i}+\sin t\text{j}\left(0\le t\le \pi \right)$

Such that

(a) the semicircle is traced counterclockwise as $\tau$ varies over the interval $\left[0,1\right]$

(b) the semicircle is traced clockwise as $\tau$ varies over the interval $\left[0,1\right]$ .