Rotation of Axes: Point (x,y) to (X,Y)

[atavistic]

Let a point be(x,y)

If the coordinate axes are shifted in clockwise direction by an angle theeta,what are the coordinate of the new point(X,Y).

 

[HallsofIvy]

How about drawing a picture. Draw the x-axis horizontal, the y-axis vertical and mark the point (x,y). Now draw the x'-axis at angle $\theta$ to the x-axis, y'-axis at angle $\theta$ to the y-axis. Draw a perpendicular to the x-axis. Its length is y. Draw a perpendicular to the x'-axis. Its length is y'. You now have two right triangles and should be able to use trig functions to deternine y' as a function of x, y, and $\theta$.