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Math Help - Problems for calculus withparametric curves.

  1. #1
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    Problems for calculus withparametric curves.

    1.Find the length of the polar curve given by on the interval .

    I know how to do it with x and y, but what to do with this one?

    Also same problem with this question

    2.For what values of on the polar curve , with , are the tangent lines horizontal? Vertical?

    Isn't just tangent=0 and tangent=1?
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  2. #2
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    Quote Originally Posted by dylan5188 View Post
    1.Find the length of the polar curve given by on the interval .

    I know how to do it with x and y, but what to do with this one?

    Also same problem with this question

    2.For what values of on the polar curve , with , are the tangent lines horizontal? Vertical?

    Isn't just tangent=0 and tangent=1?
    1. S = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} \, d\theta

    2. vertical tangent lines occur where \frac{dy}{dx} is undefined

    horizontal tangent lines occur where \frac{dy}{dx} equals zero

    \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}

    where y = r\sin{\theta} = \theta\sin{\theta}

    and x = r\cos{\theta} = \theta\cos{\theta}
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  3. #3
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    Quote Originally Posted by dylan5188 View Post
    1.Find the length of the polar curve given by on the interval .
    try L = \int_0^{\frac{1}{6}}\sqrt{1+(3.6e^{0.4\theta})^2}~  d\theta
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    2. vertical tangent lines occur where \frac{dy}{dx} is undefined

    horizontal tangent lines occur where \frac{dy}{dx} equals zero

    \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}

    where y = r\sin{\theta} = \theta\sin{\theta}

    and x = r\cos{\theta} = \theta\cos{\theta}[/quote]


    So I got theta=tantheta when horizontal tangent occur
    and theta=cotangent theta when vertical tangent occur. Then How to calculate them?
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    Quote Originally Posted by dylan5188 View Post
    2. vertical tangent lines occur where \frac{dy}{dx} is undefined

    horizontal tangent lines occur where \frac{dy}{dx} equals zero

    \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}

    where y = r\sin{\theta} = \theta\sin{\theta}

    and x = r\cos{\theta} = \theta\cos{\theta}

    So I got theta=tantheta when horizontal tangent occur
    and theta=cotangent theta when vertical tangent occur. Then How to calculate them?[/quote]

    correction ... horizontal tangent occurs when \theta = -\tan{\theta}

    have to solve these with a calculator.
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    Still dont know how to calculate
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  7. #7
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    Quote Originally Posted by dylan5188 View Post
    Still dont know how to calculate
    graph the equation y = x + \tan{x} with your graphing calculator and look for the zeros between 0 and 2\pi
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