How do you convert r^2(cos2(theta))=1 into cartesian form?
1 Answer
Feb 26, 2016
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
