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Math Help - Write Each Equation in (x,y) Form

  1. #1
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    Write Each Equation in (x,y) Form

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

    (1) r = sin(theta) + 1

    (2) r = sin(theta) - cos(theta)
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  2. #2
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    Quote Originally Posted by magentarita View Post
    The letters r and theta represent polar coordinates. Write each equation using rectangular coordinates (x,y).

    (1) r = sin(theta) + 1

    (2) r = sin(theta) - cos(theta)
    (2) Substitute x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r} and y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

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


    (1) Substitute y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

    Substitute r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2.
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    great

    Quote Originally Posted by mr fantastic View Post
    (2) Substitute x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r} and y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

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


    (1) Substitute y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

    Substitute r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2.
    Thanks for the formulas.

    Out teacher did not give us those formulas.
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  4. #4
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    Quote Originally Posted by magentarita View Post
    Thanks for the formulas.

    Out teacher did not give us those formulas.
    I'm stunned. What notes did your teacher give you for this topic?
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    Smile Wonderful....

    Quote Originally Posted by mr fantastic View Post
    (2) Substitute x = r \cos \theta \Rightarrow \cos \theta = \frac{x}{r} and y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

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


    (1) Substitute y = r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}.

    Multiply both sides by r.

    Substitute r = \sqrt{x^2 + y^2} \Rightarrow r^2 = x^2 + y^2.
    You are wonderful!
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  6. #6
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    Smile notes???

    Quote Originally Posted by mr fantastic View Post
    I'm stunned. What notes did your teacher give you for this topic?
    My teacher's notes are taken right from the textbook.

    He is lazy. He does not take time to break down the material for students.

    I am not the only student struggling in this precalculus course.
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