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Math Help - implicit differentiation, tangent line help

  1. #1
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    implicit differentiation, tangent line help

    Find the equation to the tangent and the normal to the curve  sinx siny = \frac{\sqrt{3}}{4}

    at the point (  \frac{\pi}{3} , \frac{\pi}{6} )

    I keep getting this question wrong, here's my working;

    using the product rule on sinxsiny
     sinx cosy \frac{dy}{dx} + siny cosx = 0

     \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy}

    Is this part correct?
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  2. #2
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    Quote Originally Posted by Tweety View Post
    Find the equation to the tangent and the normal to the curve  sinx siny = \frac{\sqrt{3}}{4}

    at the point (  \frac{\pi}{3} , \frac{\pi}{6} )

    I keep getting this question wrong, here's my working;

    using the product rule on sinxsiny
     sinx cosy \frac{dy}{dx} + siny cosx = 0

     \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy}

    Is this part correct?

    Yes, it is. Now just note that \frac{\cos x\sin y}{\sin x\cos y}=-\frac{\tan y}{\tan x} ...

    Tonio
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