Question

Convert y=3x+2 to a polar equation in “r” form

Answer 1

Solution.

Given

y=3x+2

We want to convert the given equation to a polar equation in “r” form

Recall that

$\begin{gathered} y=r\sin \theta \\ \text{and } \\ x=r\cos \theta \end{gathered}$$\begin{gathered} Substitu\text{ting }y=r\sin \theta\text{ and }x=r\cos \theta\text{ into }y=3x+2,\text{ we have } \\ r\sin \theta=3r\cos \theta+2 \\ r\sin \theta-3r\cos \theta=2 \\ r(\sin \theta-3\cos \theta)=2 \\ Divide\text{ both sides by }(\sin \theta-3\cos \theta) \\ r=\frac{2}{\sin \theta-3\cos \theta} \\ \\ \text{The answer is }r=\frac{2}{\sin\theta-3\cos\theta} \end{gathered}$