Convert the polar equation to rectangular form r=5cot(\theta)csc(\theta\))

Question

Convert the polar equation to rectangular form
`r=5cot(\theta)csc(\theta\))`

Answer 1

`\displaystyle x=(1)/(5)y^2`

Explanation:

`\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr((\cos(\theta))/(\sin(\theta))\biggr)\biggr((1)/(\sin(\theta))\biggr)\\\\r=(5\cos(\theta))/(\sin^2(\theta))\\\\r^2=(5r\cos(\theta))/(\sin^2\theta)\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=(1)/(5)y^2`