Answer
$$x= R\cos( \frac{2\pi t}{10}), \quad y= -R\sin(-\frac{2\pi t}{10}), \quad t\in [0,2\pi].$$
Work Step by Step
The parametric equations with counter-clockwise orientation that describe a full circle of radius $R$, centered at the origin are
$$x=R\cos t, \quad y=R\sin t, \quad t\in [0,2\pi].$$
Now, to get the clockwise orientation with the parameter varies over the interval $[0, 10]$ we have $$x=R\cos(- \frac{2\pi t}{10})=R\cos( \frac{2\pi t}{10}),\\ \quad y=R\sin(- \frac{2\pi t}{10})=-R\sin(-\frac{2\pi t}{10}), \quad t\in [0,2\pi].$$
