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Cam you get me started with 11 and 13 by providing the first 2 steps? I will then try solving the problems on my own.
11.
r=3cos(2θ)
first apply the formula cos(2θ)=cos^2(θ)-sin^2(θ)
r= 3cos^2(θ)-3sin^2(θ)
then use
x=rcos(θ) and y=rsin(θ)
you continue
13.
r^2=8/(2-sin^2(θ))
From x=rcos(θ) and y=rsin(θ), we have that
cos(θ)= x/r
sin(θ)= y/r
tan(θ)= y/x
cot(θ)= x/y
The input becomes
r^2 =8/(2- y^2/r ^2)
you continue
11. need to finish, answer cannot have r , only x and y
13. correct
11.
View attachment 2246
substitute View attachment 2247
View attachment 2248........ both sides raise to power of 3
View attachment 2251
View attachment 2254
View attachment 2257