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Math Help - Find the value K

  1. #1
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    Find the value K

    If <br />
siny = xsin(a+y)<br />
and <br />
\frac{dy}{dx} = K \frac{sin^2y}{x^2}<br />
, find K
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  2. #2
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    Quote Originally Posted by zorro View Post
    If <br />
siny = xsin(a+y)<br />
and <br />
\frac{dy}{dx} = K \frac{sin^2y}{x^2}<br />
, find K
    I'm assuming that a is constant. If we expand your sine relationship and divide by x then \frac{\sin y}{ x} = \sin a \cos y + \cos a \sin y then divide by \sin y so

    \sin a \cot y + \cos a = \frac{1}{x} and upon differentiation gives - \sin a \csc^2 y y' = - \frac{1}{x^2} which solving for y ' gives

     y' = \frac{1}{\sin a} \frac{\sin^2 y}{x^2}

    in which we can identify K.
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  3. #3
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    Thanks mite....

    Quote Originally Posted by Danny View Post
    I'm assuming that a is constant. If we expand your sine relationship and divide by x then \frac{\sin y}{ x} = \sin a \cos y + \cos a \sin y then divide by \sin y so

    \sin a \cot y + \cos a = \frac{1}{x} and upon differentiation gives - \sin a \csc^2 y y' = - \frac{1}{x^2} which solving for y ' gives

     y' = \frac{1}{\sin a} \frac{\sin^2 y}{x^2}

    in which we can identify K.

    thanks mite
    cheers
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