The new coordinates (X,, Y,) of a point in the x-y plane that is rotated aboutthe z axis

Chapter 7, Problem 39

(choose chapter or problem)

The new coordinates (X,, Y,) of a point in the x-y plane that is rotated aboutthe z axis at an angle e (positive is clockwise) are given byX, = X0cos9- Y0sin9Y, = X0sin9 + Y0cos9where (X0, Y0) are the coordinates of the point before the rotation. Write auser-defined function that calculates (X7, Y7) given (X0, Y0) and e. For functionname and arguments, use [xr I yr] =rotation (xl y I q), where theinput arguments are the initial coordinates and the rotation angle in degreesand the output arguments are the new coordinates.(a) Use rotation to determine the new coordinates of a point originally at(6.5, 2.1) that is rotated about the z-axis by 25.(b) Consider the function y = (x -7)2 + 1.5 for 5 :5: x :5: 9. Write a program ina script file that makes a plot of the function. Then use rotation to rotateall the points that make up the first plot and make a plot of the rotated function.Make both plots in the same figure and set the range of both axes at 0 to10.