37-Calculus-of-ParametricEq-Working

# Time by noting that from the derivative formula dy dt

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• hain2005
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time by noting that: From the derivative formula dy dt dx dt dy dx = you can make the following observations: For horizontal slope where 0 dy dx = the only way this can happen is when 0 dy dt = For vertical slope where dy undefined dx = the only way this can happen is when 0 dx dt = You can use these rules when the problem asks for horizontal and vertical tangent without having to find dy dx . If the problem asks for a generic slope, then you must find dy dx . For example: For the parametric equation 3 3 4cos 4sin x t y t = = Find the equation for the tangent at / 3 t π = Here, you have to find tan( ) dy t dx = − . Hence the slope at / 3 t π = is tan( ) 3 3 dy m dx π = = = You need the point to finish the problem. at / 3 t π = , the point is: 3 3 1 4cos 2 3 3 4sin 2 x t y t = = The problem now becomes a standard Algebra problem: Find the equation for the line having a slope 3 m = − and going through the point 1 3 3 , 2 2 . And you should be able to complete it from here.
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