Convert to Polar Form...3

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Mar 19, 2022.

  1. nycmathguy

    nycmathguy

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    Screenshot_20220311-155742_Samsung Notes.jpg

    IMG_20220319_133410.jpg

    IMG_20220319_133426.jpg

    IMG_20220319_133438.jpg
     
    nycmathguy, Mar 19, 2022
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  2. nycmathguy

    MathLover1

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    19.
    y^2 =x^3

    In polar coordinates, x=r*cos(θ) and y=r*sin(θ).

    Thus, the input can be rewritten as

    r^2sin^2(θ)=r^3cos^3 (θ)

    r^2sin^2(θ)-r^3cos^3 (θ)=0

    Simplify:

    r^2(sin^2(θ)-rcos^3(θ))=0

    20.

    y=x^2

    In polar coordinates, x=rcos(θ) and y=rsin(θ).

    Thus, the input can be rewritten as

    rsin(θ)=(rcos (θ))^2

    rsin(θ)=r^2cos^2 (θ)

    sin(θ)=rcos^2 (θ)

    r=sin(θ)/cos^2(θ)


     
    MathLover1, Mar 19, 2022
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Ok. Thank you. I did my best to work out the problems.
     
    nycmathguy, Mar 19, 2022
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