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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- Jan 26th 2010, 11:11 AMdynamohow 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.

- Jan 27th 2010, 01:55 AMCorum
Are you familier with polar coordinates?

Imagine your equation for the curve. Y=...? in polar coordinates (with x=r cos $\displaystyle \theta$ and y=r sin $\displaystyle \theta$) it is expressed in r(distance from origin) and $\displaystyle \theta$, angle created with oX+. with this it's easy to change $\displaystyle \theta$ to the appropriate angle.

I hope this helps - Jan 27th 2010, 02:29 AMHallsofIvy
Dynamo, to rotate y= f(x) through angle $\displaystyle \theta$, around the origin, replace x with $\displaystyle x'= x cos(\theta)+ y sin(\theta)$ and y with $\displaystyle y= -x sin(\theta)+ y cos(\theta)$.

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

That is, replace x with $\displaystyle x'= (x- x_0)cos(\theta)+ (y- y_0)sin(\theta)+ x_0$ and replace y with $\displaystyle y'= -(x- x_0)sin(\theta)+ (y- y_0)cos(\theta)+ y_0$ - Jan 27th 2010, 04:15 AMdynamo
- Jan 27th 2010, 04:32 AMdynamothanks