how to rotate a curve

**dynamo** · January 26th 2010, 11:11 AM

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.

**Corum** · January 27th 2010, 01:55 AM

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

**HallsofIvy** · January 27th 2010, 02:29 AM

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 $y'= -(x- x_0)sin(\theta)+ (y- y_0)cos(\theta)+ y_0$

**dynamo** · January 27th 2010, 04:15 AM

Originally Posted by Corum

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

**dynamo** · January 27th 2010, 04:32 AM

Originally Posted by HallsofIvy

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

Thread: how to rotate a curve

LinkBack

Thread Tools

Display

how to rotate a curve

thanks

Similar Math Help Forum Discussions

Rotate Vector

volumes rotate about y = x

controversy from how to rotate curve thread

rotate conic

Using sin and cos to rotate a point

Search Tags