r=sin4theta with rectangular coordinates?

r = 4 sintheta with rectangular coordinates?

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  • 1 decade ago
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    Polar coordinates consists of:

    r = radius measure(magnitude)

    theta = angle measure(degrees or rad's)

    So according to your question, you have stated that r = 4 sintheta :

    So the radius(r) = 4*sin(theta)

    And Angle measure = theta

    To convert the above polar coordinates to Rectangular coordinates:

    where Rectangular coordinates = (a, ib)

    where a = real number along the x=axis

    and ib = imaginary number along the y-axis

    i = imaginary number(sqrt(-1)) ( y-axis)

    if you remeber your unit circle, and a little bit of trigonometry:

    sin(theta) = opp/hyp

    cos(theta) = adj/hyp

    Hence:

    opp = hyp*sin(theta)

    adj = hyp*cos(theta)

    So since, a = adj

    ib = opp

    r = hyp

    Your Rectangular coordinates ( a , ib)

    is now ( r*cos(theta) , r*sin(theta)

    Finally: your answer, with r = 4 sintheta

    ( 4 sintheta*cos(theta) , 4 sintheta*sin(theta)

    ( 4 sintheta*cos(theta) , 4 sin^2(theta) )

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  • Mark
    Lv 4
    1 decade ago

    r = 4 sinθ

    multiply both sides by r

    Substitute:

    r² = 4r sinθ

    Substitute:

    r² = (x² + y²)

    y = rsinθ

    (x² + y²) = 4y

    x² + y² - 4y = 0

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