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Math Help - Finding an equation tangent line

  1. #1
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    Finding an equation tangent line

    Hello everyone

    How would i solve the following

    Find an equation for the tangent line to the graph of x+sin(y-2x)=1 at the point (1,2)

    I did

    1+cos(y-2x)(dy/dx)(-2)=0

    then I did cos(y-2x)(dy/dx)=2

    (dy)/(dx)=(2)/(cos(y-2x) so would I just plug in the value of x and y.
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  2. #2
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    Re: Finding an equation tangent line

    That would give you the slope. You need the equation for the tangent line. The equation of a line through (x_0,y_0) with slope m is (y-y_0)=m(x-x_0).

    - Hollywood
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  3. #3
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    Re: Finding an equation tangent line

    Quote Originally Posted by homeylova223 View Post
    Hello everyone

    How would i solve the following

    Find an equation for the tangent line to the graph of x+sin(y-2x)=1 at the point (1,2)

    I did

    1+cos(y-2x)(dy/dx)(-2)=0

    then I did cos(y-2x)(dy/dx)=2
    This is incorrect. from 1+ cos(y- 2x)(dy/dx)(-2)= 0 you get -2cos(y- 2x)(dy/dx)= -1 or cos(y- 2x)(dy/dx)= 1/2. When x= 1, y= 2, cos(2- 1)(dy/dx)= 1/2 so dy/dx= 1/cos(1).

    (dy)/(dx)=(2)/(cos(y-2x) so would I just plug in the value of x and y.
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  4. #4
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    Re: Finding an equation tangent line

    the Gradient is 1 and the equation of the tangent is x-y=-1.
    Thanks from hollywood
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  5. #5
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    Re: Finding an equation tangent line

    There is a slight problem, when you differentiate you will get
    1 + cos ( y - 2x ) [ dy/dx -2] = 0
    At ( 1,2 ) we get dy/dx = 1
    So the equation of tangent is ( y-2) = 1 * ( x-1)
    OR
    x - y + 1 = 0
    Thanks from hollywood
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  6. #6
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    Re: Finding an equation tangent line

    Yeah, \frac{dy}{dx}=1. Sorry I missed that.

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