Ledsnyder said: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)
Ledsnyder said:I have the equations.I just don't know how to find the new equation based on the coordinates.
The general form of a polynomial function is f(x) = anxn + an-1xn-1 + ... + a1x + a0, where an is the leading coefficient, n is the degree of the polynomial, and a0 is the constant term.
The degree of a polynomial function is the highest exponent in the function. In this case, the degree is 3 because the term with the highest exponent is 5x3.
The rotation of axes is a transformation that allows us to change the orientation of the coordinate system, making it easier to graph certain functions. In this case, rotating the axes can help us graph the polynomial function 5x^3+10x^2+20x+15 in a more convenient way.
To rotate the axes, we use the rotation matrix [cosθ -sinθ; sinθ cosθ], where θ is the angle of rotation. We multiply this matrix by the coordinates of each point in the original graph to obtain the coordinates of the rotated points. This will result in a new graph with a rotated coordinate system.
Yes, you can rotate the axes of any polynomial function. However, it may not always be necessary or helpful to do so. It depends on the function and the purpose of the graph. In some cases, it may be easier to graph the function without rotating the axes.