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Calc 2

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Find a Cartesian equation for the polar curve y = 5tan(theta)sec(theta). I think I got it but I just wanted to double check. Thanks in advance!

  • Calc 2 -

    Would you like to post your answer if you just wanted to check?

  • Calc 2 -

    y=... or r=...?

  • Calc 2 -

    It would be in the form:
    x=f(θ),
    y=g(θ)
    where f and g are functions of θ.

  • Calc 2 -

    Read the terms of your problem!

  • Calc 2 -

    If r=tan(theta)sec(theta)
    then r(cos(theta)^2)=sin(theta)
    (r*cos(theta))^2=r*sin(theta)
    x^2 = y

  • Calc 2 -

    I am sorry, it is r = 5tan(theta)sec(theta)

  • Calc 2 -

    Mggraph: but (r*cos(theta))^2 is not x^2, is it? I thought rcos(theta) = x^2

    This is what I got:

    1 = 5y/[(x^2)(square root of(x^2 + y^2))]

  • Calc 2 -

    Then all right sides multiply by 5:
    x^2=5y or
    y=0.2x^2

  • Calc 2 -

    Aha I got it! Thanks so much! :)

  • Calc 2 -

    if I've this equation: r=sec theta tan theta. How is?

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