Finding point coordinates after canvas rotation

I have an image with known coordinates of multiple points within it.
I need to find a new position for each of the point after I rotate the canvas of the image a certain degree around the center.
Anyone has a way to calculate it?
I am working on a project of mapping multiple land-maps to position on Google-map but the axis is not matching.
Rotating the image itself is not good as it distorts the text.
Best way is to virtually rotate the image to match the google-mp alignment and then draw poligons on google-map after rotation.
But I need to find coordinates of each point after I rotate the original image around its center.
I know I shoudl probably treat the image as a circle and re-calculate each point after finding its center but I need a formula.
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Commented:
xnew=center+((xold-center)*cos(degrees*pi/180)-(yold-center)*sin(degrees*180/pi))
ynew=center+((yold-center)*cos(degrees*pi/180)+(xold-center)*sin(degrees*180/pi))
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