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massively confused with C3 differentiation involving radians watch

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    I have an equation of the curve 'x = 2siny'

    I have to show that 'dy/dx = 1/square root of 2' at point 'p' on the curve

    point 'p' is: (square root of 2, pi/4)

    The equation has 'x =...' instead of the usual 'y=....', so how do I differentiate 'x = 2siny'.

    after I differentiated it, do I sub in the 'x' or 'y' co-ordinates of point 'p' into it ???

    ________________________________ __________________________

    I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
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    You've got the equation x=2siny.

    Find dx/dy (instead of dy/dx), because you can do this like you would normally (in other words, pretend x is y and y is x in the equation above.

    Then use the fact that dy/dx = 1 / (dx/dy).

    Then evaluate your expression for dy/dx at y=pi/4 (the y coordinate of the point p).
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    (Original post by Drederick Tatum)
    You've got the equation x=2siny.

    Find dx/dy (instead of dy/dx), because you can do this like you would normally (in other words, pretend x is y and y is x in the equation above.

    Then use the fact that dy/dx = 1 / (dx/dy).

    Then evaluate your expression for dy/dx at y=pi/4 (the y coordinate of the point p).

    so, once I have diferentiated the equation like I would normally do with x's, I just put it below '1' in a fraction?

    btw I never knew dy/dx = 1 / (dx/dy)
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    What about the 2nd question?

    I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
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    (Original post by PRudd)
    What about the 2nd question?

    I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
    yeah, I know I could use 'dx/dy' for the equation 'x = cos(2y+pi). But I am not sure how to differentiate 'pi'.
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    pi is just a constant between 3 and 4. So d/dx(pi) = 0
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    (Original post by Drederick Tatum)
    pi is just a constant between 3 and 4. So d/dx(pi) = 0
    But can cos(2y+pi) be split when differentiating?
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    (Original post by W.H.T)
    ...I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
    I know whats going on now

    dx/dy = -2Sin(2y + Pi)

    Put in value of y. This gives dx/dy = 2

    This means that dy/dx =0.5 and then you can use y-y1 = m(x-x1) to get the final equation.

    Phew... I can sleep happy :yes:
 
 
 
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Updated: January 17, 2010
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