Different Representation of Curves – Switch from parametric to Cartesian – Exercise 3748

Exercise

Given the vector function in parameter representation (with parameters t and a)

$$\vec{r}(t)=a(t-\sin t)\vec{i}+a(1-\cos t)\vec{j}$$

$$a>0$$

The range of parameter t is

$$-\infty< t<\infty$$

Present the curve in the Cartesian presentation and describe the curve graph.

$$x(t)=a(t-\sin t)$$
$$y(t)=a(1-\cos t)$$