Given:
Given that
[tex]r=\frac{5}{3\sin\theta-\cos\theta}[/tex]
Required: Convert to rectangular form.
Explanation:
The given equation in polar can be written as
[tex]\begin{gathered} r(3\sin\theta-\cos\theta)=5 \\ 3r\sin\theta-r\cos\theta=5 \end{gathered}[/tex]
Substitute
[tex]x=r\cos\theta,y=r\sin\theta[/tex]
Then the equation becomes 3y - x = 5.
Solve for y.
[tex]\begin{gathered} 3y=x+5 \\ y=\frac{1}{3}x+\frac{5}{3} \end{gathered}[/tex]
Final Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
