Solving Trig Transformations: Rotation of a Point

[smileandbehappy]

Homework Statement

A point with coordinates x and y is rotated in an anticlockwise direction through an angle z, so that its distance from the origin of the coordinate system remains constant. Show that the new x and y coordinates become

xcosz - ysinz and xcosz + ysinz respectively.

Homework Equations

The Attempt at a Solution

Well I am looking for some advice on how to start this! The wording is confusing to me! To my mind surely if you rotate a point it will be exactly the same? Any help would be supremely appretiated.

 

[Integral]

By rotating a point, they mean it is rotated about the origin by a angle z. start by drawing a picture, show the x and y components at each location. Now study the pic until you can identify the relationships.