Answer
$x=(a+b)cos\theta - b\cdot cos(\frac{a+b}{b}\theta)$
$y=(a+b)sin\theta - b\cdot sin(\frac{a+b}{b}\theta)$
Work Step by Step
This problem is similar to Exercise 63, except that the circle C is rolling outside the big circle.
So we need to modify the equations in Exercise 63. The first difference is that the $(a-b)$ term in the front of the
equations become $(a+b)$, and the second difference is that the angle inside the last term changed from
$(\alpha-\theta)=(\frac{a}{b}\theta-\theta)$ to $(\pi-\alpha-\theta)=(\pi-\frac{a}{b}\theta-\theta)$ (This is because when circle C is rolling outside, angle OCP will be $\alpha$, see figure in Exercise 63). Thus we can write the epicycloid equations as $x=(a+b)cos\theta - b\cdot cos(\frac{a+b}{b}\theta)$ and $y=(a+b)sin\theta - b\cdot sin(\frac{a+b}{b}\theta)$
