Question

How do you convert `r^2(cos2(theta))=1` into cartesian form?

Answer 1

`x^2 = y^2`

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

`• x = rcostheta rArr costheta = x/r`

`• y = rsintheta rArr sintheta = y/r`

and `color(blue)" Double angle formula "`

`• cos(2theta) = cos^2theta - sin^2theta`

hence `: r^2(cos(2theta)) = r^2( cos^2theta - sin^2theta) = 1`

`rArr r^2(x^2/r^2 - y^2/r^2 ) = 1`

and 'taking out' `1/r^2 " as a common factor "`

`rArr cancel(r^2)/cancel(r^2) (x^2 - y^2) = 1 rArr x^2 = y^2`