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Math Help - Write Using (r, theta)

  1. #1
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    Smile Write Using (r, theta)

    The letters x and y represent the rectangular coordinates. Write each equation using polar corrdinates (r, theta).

    (1) 4x^(2) y = 1

    (2) y = -3
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  2. #2
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by magentarita View Post
    The letters x and y represent the rectangular coordinates. Write each equation using polar corrdinates (r, theta).

    (1) 4x^(2) y = 1

    (2) y = -3
    The second one is r\cos(\theta-3\pi/2)=3.
    Also see the following figure:
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    The letters x and y represent the rectangular coordinates. Write each equation using polar corrdinates (r, theta).

    (1) 4x^(2) y = 1

    (2) y = -3
    I'll try (2):
    When converting from rectangular coordinates to polar keep these three things in mind.

    1. x=r \cos \theta

    2. y=r \sin \theta

    3. r^2 = x^2+y^2

    y=r \sin \theta

    Substituting,

    r \sin \theta = -3
    r=-\frac{3}{\sin \theta}=-3 \csc \theta
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    The letters x and y represent the rectangular coordinates. Write each equation using polar corrdinates (r, theta).

    (1) 4x^(2) y = 1

    (2) y = -3

    Okay, here's (1):

    4(r\cos\theta)^2 \cdot r\sin\theta=1
    4r^2\cos^2\theta \cdot r \sin\theta=1
    4r^3\cos^2\theta \sin\theta=1
    r^3=\frac{1}{4\cos^2 \theta \sin \theta}

    r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}
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  5. #5
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    Thank you

    Quote Originally Posted by bkarpuz View Post
    The second one is r\cos(\theta-3\pi/2)=3.
    Also see the following figure:
    Thank you for your help and for taking time out to form a picture.
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  6. #6
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    Again...

    Quote Originally Posted by masters View Post
    I'll try (2):
    When converting from rectangular coordinates to polar keep these three things in mind.

    1. x=r \cos \theta

    2. y=r \sin \theta

    3. r^2 = x^2+y^2

    y=r \sin \theta

    Substituting,

    r \sin \theta = -3
    r=-\frac{3}{\sin \theta}=-3 \csc \theta
    Your help is wonderful. I can now use your steps to answer similar questions.
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  7. #7
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    Fabulous!

    Quote Originally Posted by masters View Post
    Okay, here's (1):

    4(r\cos\theta)^2 \cdot r\sin\theta=1
    4r^2\cos^2\theta \cdot r \sin\theta=1
    4r^3\cos^2\theta \sin\theta=1
    r^3=\frac{1}{4\cos^2 \theta \sin \theta}

    r=\sqrt[3]{\frac{1}{4\cos^2 \theta \sin \theta}}
    Your math help is very much appreciated.
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