Rotation of Axes: 5x^3+10x^2+20x+15

[Ledsnyder]

Homework Statement

5x^3+10x^2+20x+15 is rotated through the angle 45 degrees to new xy coordinate system.Whats the equation to the coordinate system?

Homework Equations

The Attempt at a Solution

New X= xcos(theta)+ycos(theta) New Y=-xsin(theta)+ycos(theta)

 

[Ray Vickson]

Homework Statement

5x^3+10x^2+20x+15 is rotated through the angle 45 degrees to new xy coordinate system.Whats the equation to the coordinate system?

Homework Equations

The Attempt at a Solution

New X= xcos(theta)+ycos(theta) New Y=-xsin(theta)+ycos(theta)

So...? Show the rest of your work.

 

[Ledsnyder]

I have the equations.I just don't know how to find the new equation based on the coordinates.

 

[Ray Vickson]

I have the equations.I just don't know how to find the new equation based on the coordinates.

What is preventing you from putting in $y = 5x^3+10x^2+20x+15$ into the expressions for $X$ and $Y$? This will, at least, give you a "parametric" form of the relationship between $X$ and $Y$ along the curve (the parameter will be $x$). It might be harder if you want an explicit formula of the form $Y = f(X)$ (or maybe $G(X,Y) = 0$) in which the parameter $x$ has been eliminated, but I suggest you give it a try. Or have you already done that?