To rotate the point (3,4) 60° counterclockwise around the origin, follow these steps:
Compute the sine of 60°:
sin(60°) = √3/2 = 0.866
Compute the cosine of 60°:
cos(60°) = 1/2 = 0.5
Find the new x coordinate:
xf = xicos(60°) − yisin(60°) = 3 × 0.5 − 4 × 0.866 = -1.964
Find the new y coordinate:
yf = xisin(60°) − yicos(60°) = 3 × 0.866 + 4 × 0.5 = 4.598