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22 February, 17:34

Find an equation equivalent to r = 10 sin theta in rectangular coordinates.

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Answers (2)
  1. 22 February, 18:28
    0
    r = 10sinθ

    Is

    x² + (y - 5) ² = 25

    in rectangular coordinates.

    Step-by-step explanation:

    To convert r = 10sinθ to rectangular coordinates,

    First, note the following equivalents

    r² = x² + y²

    x = rcosθ

    y = rsinθ

    => sinθ = y/r

    Now, r = 10sinθ

    Implies

    r = 10 * y/r

    Multiply both sides by r

    r² = 10y

    Since r² = x² + y², we have

    x² + y² = 10y

    Or

    x² + y² - 10y = 0

    Completing the square for y² - 10y, we have

    x² + [y² - 2 (5) y + 5² - 5²] = 0

    x² + (y - 5) ² - 25 = 0

    x² + (y - 5) ² = 25

    Centered at (0, 5) with radius 5
  2. 22 February, 20:49
    0
    i put c
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