It reads: When you rotate the x-y coordinate system by an angle of $\displaystyle \theta$, the new cordinates x' and y' can be calculated using the following expressions:

x'= xCos$\displaystyle \theta$+ ysin$\displaystyle \theta$ (1)

y'=-xsin$\displaystyle \theta$ + ycos$\displaystyle \theta$(2)

Given that you know the rotated coordinates x' and y' and the rotation angle $\displaystyle \theta$ how do you calculate the original x an y? (in other words, how do you express x and y using x', y' and $\displaystyle \theta$?

Hint: rearrange equations (1) and (2) so that x and y can be expressed using x', y', sin$\displaystyle \theta$ and cos$\displaystyle \theta$

and thats all it gives me except for the addition of another example problem which asks

if x'=24, y'=-3 and $\displaystyle \theta$=30 degrees, what are the values of x and y?

many thanks, also what are these problems trying to show im not really sure what they have to do with college algebra.