Question

Find parametric equation of x=a(1+cos theta)

Answer 1

Given polar form of equation of cardioid

$$r=a(1+\cos \theta)$$

We have that

$$x=r\cos \theta$$

$$y=r\sin \theta$$

Substitute

$$x=a\cos \theta(1+\cos \theta)$$

$$y=a\sin \theta(1+\cos \theta)$$

Replace $\theta$ with $t$ . The parametric equation is

$$\begin{matrix} x=a\cos t(1+\cos t)\\ y=a\sin t(1+\cos t) \end{matrix}$$