I have been trying to convert the polar equation to rectangular.
$U(1,\theta) = 10+3*sin(\theta)-10*cos(2*\theta)$
I started off my multiplying everything by r and using the trig identity for cos($2*\theta$).
$= 10 * r +3* r *sin(\theta)-10*r*(2*cos^2(\theta)-1)$
Then I distributed everything out.
$= 10 * r +3* r *sin(\theta)-20*r*cos^2(\theta) + 10*r$
Combined like terms.
$= 20* r + 3* r *sin(\theta) - 20*r*cos^2(\theta)$
At this point if I use
$x^2+y^2 =r^2$
x = rcosθ
y = rsinθ
y/x =tanθ
I get a bit confused because I end up with the $r*cos^2(\theta)$ term where I am unable to do anything.
Any explanation will help.
Thanks, Mary