It is just reversing the procedure.

To get the (x',y') from (x,y) with a rotation of theta, the following were derived:

x'= xCos(t) + ysin(t) --------(1)

y'= -xsin(t) + ycos(t) ..........(2)

So if you reverse the procedure, to get back to the (x,y), you use

x = x'Cos(-t) + y'sin(-t) --------(3)

y'= -x'sin(-t) + y'cos(-t) ..........(4)

where the angle of rotation is the reverse of the theta before.

Rewriting those, in terms of the original theta,

x = x'cos(t) -y'sint(t) -------(3a)

y = x'sin(t) +y'cos(t) --------(4a)

that is because cos(-t) = cos(t), and sin(-t) = -sin(t).

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'"if x'=24, y'=-3 and =30 degrees, what are the values of x and y?"

x = 24cos(30deg) -(-3)sin(30deg) = 22.28461

y = 24sin(30deg) +(-3)cos(30deg) = 9.40192

Maybe you want to check if (22.28461,9.40192) will become (24,-3) if the original axes are rotated by 30 degrees.