Question

I need help with this practice problem solving The subject, I believe, is complex numbers and vectors

Answer 1

Given:

Given that

`r=(5)/(3\sin\theta-\cos\theta)`

Required: Convert to rectangular form.

Step-by-step explanation:

The given equation in polar can be written as

`\begin{gathered} r(3\sin\theta-\cos\theta)=5 \\ 3r\sin\theta-r\cos\theta=5 \end{gathered}`

Substitute

`x=r\cos\theta,y=r\sin\theta`

Then the equation becomes 3y - x = 5.

Solve for y.

`\begin{gathered} 3y=x+5 \\ y=(1)/(3)x+(5)/(3) \end{gathered}`

Final Answer:

`y=(1)/(3)x+(5)/(3)`