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Math Help - how to rotate a curve

  1. #1
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    how to rotate a curve

    how do you rotate a curve ,whether it is a quadratic ,parabolic any type of curve and get the equation of the new/transformed curve,after rotating by x degrees.
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  2. #2
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    Are you familier with polar coordinates?
    Imagine your equation for the curve. Y=...? in polar coordinates (with x=r cos \theta and y=r sin \theta) it is expressed in r(distance from origin) and \theta, angle created with oX+. with this it's easy to change \theta to the appropriate angle.
    I hope this helps
    Last edited by Corum; January 27th 2010 at 03:48 AM.
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  3. #3
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    Dynamo, to rotate y= f(x) through angle \theta, around the origin, replace x with x'= x cos(\theta)+ y sin(\theta) and y with y= -x sin(\theta)+ y cos(\theta).

    To rotate y= f(x) through angle \theta, about point (x_0, y_0), first translate [tex](x_0, y_0) to the origin by subtracting x_0 from x and y_0 from y, then do the rotation, then translate back.

    That is, replace x with x'= (x- x_0)cos(\theta)+ (y- y_0)sin(\theta)+ x_0 and replace y with y'= -(x- x_0)sin(\theta)+ (y- y_0)cos(\theta)+ y_0
    Last edited by HallsofIvy; January 27th 2010 at 06:24 AM.
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  4. #4
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    Quote Originally Posted by Corum View Post
    Are you familier with polar coordinates?
    Imagine your equation for the curve. Y=...? in polar coordinates (with x=r cos \theta and y=r sin \theta) it is expressed in r(distance from origin) and \theta, angle created with oX+. with this it's easy to change \theta to the appropriate angle.
    I hope this helps
    thanks
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  5. #5
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    thanks

    Quote Originally Posted by HallsofIvy View Post
    Corum, on this forum use "\", not "#". Also, the final "/MATH must be completely inclosed in [ ].

    "[ math ] \theta [ /math ] (without the spaces) gives \theta.

    To see the LaTex code for any expression in a post, click on that expression.

    Dynamo, to rotate y= f(x) through angle \theta, around the origin, replace x with x'= x cos(\theta)+ y sin(\theta) and y with y= -x sin(\theta)+ y cos(\theta).

    To rotate y= f(x) through angle \theta, about point [tex](x_0, y_0), first translate [tex](x_0, y_0) to the origin by subtracting x_0 from x and y_0 from y, then do the rotation, then translate back.

    That is, replace x with x'= (x- x_0)cos(\theta)+ (y- y_0)sin(\theta)+ x_0 and replace y with y'= -(x- x_0)sin(\theta)+ (y- y_0)cos(\theta)+ y_0
    thanks
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