Question

A 36 degree counterclockwise rotation centered at the origin sends the point A = (6,3) to the image point B. To three decimal places, find the coordinates of B.

Answer 1

we can form a rotation setup using sum of cosine and sine functions

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

x' = cos(a+b) ; x = cos(a)
y' = sin(a+b) ; y = sin(a)

sub them in

x' = x cos(b) - y sin(b)
y' = y cos(b) + x sin(b)