Convert to Rectangular Form...7

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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.



Screenshot_20220311-155740_Samsung Notes.jpg
 
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.

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

IMG_20220319_123140.jpg


IMG_20220319_123154.jpg


IMG_20220319_123209.jpg
 
11.
upload_2022-3-19_12-42-41.gif


substitute
upload_2022-3-19_12-43-23.gif


upload_2022-3-19_12-44-5.gif
........ both sides raise to power of 3


upload_2022-3-19_12-46-57.gif


upload_2022-3-19_12-48-29.gif



upload_2022-3-19_12-49-57.gif
 

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