Question

Convert polar equation to rectangular equation.
r = csc(theta) + sec(theta)

Answer 1

\[\Large\rm r=\csc \theta+\sec \theta\]\[\Large\rm r=\frac{1}{\sin \theta}+\frac{1}{\cos \theta}\]Multiply both sides by sine and cosine,\[\Large\rm r \sin \theta \cos \theta=\cos \theta + \sin \theta\]Multiply both sides by r,\[\Large\rm (r \sin \theta)(r \cos \theta)=r \cos \theta+ r \sin \theta\]Then use these to convert from `Polar` to `Cartesian`,\[\Large\rm x=r \cos \theta, \qquad\qquad y=r \sin \theta\]