Question

Explain how to use parametric equations to transform a

polar function $r=f\left(\theta \right)$

Short answer

The parametric equations are$x=(1-\sin \theta )\cos \theta ,y=(1-\sin \theta )\sin \theta$

Step-by-step solution

Given information 

The polar function is$r=f\left(\theta \right)$

The objective is to transform the polar equation of the form r=f(θ)  into the parametric equations.

The function $r=f\left(\theta \right)$is simply expressed using parametric equations of the form $x=x\left(\theta \right),y=y\left(\theta \right)$where $\theta$is the parameter.

To convert polar coordinates into rectangle coordinates$x=r\cos \theta ,y=r\sin \theta$

 write the parametric equations for r=1-sinθ 

If $r=f\left(\theta \right)$then,

$x=f\left(\theta \right)\cos \theta ,y=f\left(\theta \right)\sin \theta .$

The parametric equations for $r=1-\sin \theta$

The parametric equations have the following form:

$x=f\left(\theta \right)\cos \theta ,y=f\left(\theta \right)\sin \theta$

Then the parametric equations are:

$x=(1-\sin \theta )\cos \theta ,y=(1-\sin \theta )\sin \theta$