Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

r=sin4theta with rectangular coordinates?

r = 4 sintheta with rectangular coordinates?

2 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    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) )

  • 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

Still have questions? Get your answers by asking now.