Convert to Rectangular Form...7

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

 

Can you finish 11 for me? I can't further simplify.

 

11.


substitute

........ both sides raise to power of 3

 

Wow! Awesome! Thank you.