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Math Help - Calculus ( finding tangent to the curve question)

  1. #1
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    Question Calculus ( finding tangent to the curve question)

    Hi, I just can't do this question and i am not sure where i am getting it wrong.

    4. Find the equation of the tangent to the curve x = cos ( 2y + pi) at (0, pi/4).

    Give your answer in the form y= ax + b where a and b are constants to be found.

    I have no idea how to get the gradient....

    Please show your working.

    Thanks a lot.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Changhons View Post
    Hi, I just can't do this question and i am not sure where i am getting it wrong.

    4. Find the equation of the tangent to the curve x = cos ( 2y + pi) at (0, pi/4).

    Give your answer in the form y= ax + b where a and b are constants to be found.

    I have no idea how to get the gradient....

    Please show your working.

    Thanks a lot.
    Taking the derivative we get

    \frac{d}{dx} x =\frac{d}{dx}( cos(2y+\pi))

    1=-\sin(2y+\pi)(2\frac{dy}{dx})

    Now we evaluate (0,pi/4) to get

    1=-2y' \sin\left( \frac{3\pi}{2}\right))

    1=-2y'(-1) \iff y'=\frac{1}{2}

    I hope this helps
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  3. #3
    MHF Contributor

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    You could also just use m= dx/dy and write the equation of the line as x= my+ \pi/4.
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