Question

Question #785b9

Answer 1

`r = sqrt(3/(cos(theta)sin(theta)))`

Explanation:

Let's begin by show the graph of the original equation, `xy=3`:

Substitute `rcos(theta)` for x and `rsin(theta)` for y:

`rcos(theta)rsin(theta)=3`

Solve for r:

`r^2= 3/(cos(theta)sin(theta))`

`r = sqrt(3/(cos(theta)sin(theta)))`

Please observe that the graph of the above equation is identical to the original:

This proves that the conversion is correct.