# Rotation of axes

1. Sep 7, 2014

### Ledsnyder

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. The attempt at a solution
New X= xcos(theta)+ycos(theta) New Y=-xsin(theta)+ycos(theta)

2. Sep 7, 2014

### Ray Vickson

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

3. Sep 7, 2014

### Ledsnyder

I have the equations.I just dont know how to find the new equation based on the coordinates.

4. Sep 7, 2014

### Ray Vickson

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?