Question

How do you convert `x^2=3y` to polar form?

Answer 1

`r=3tanthetasectheta`

Explanation:

To convert from `color(blue)"cartesian to polar form"`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))`

`rArr(rcostheta)^2=3(rsintheta)`

`rArrr^2cos^2theta=3rsinthetarArrrcos^2theta=3sintheta`

`rArrr=(3sintheta)/cos^2theta=(3sintheta)/costhetaxx1/costheta`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(tantheta=(sintheta)/(costheta)" and " sectheta=1/(costheta))color(white)(a/a)|)))`

`rArrr=3tanthetasectheta`