Use the angle-sum identity for cosine:

You may also think of the unit circle. Pick an arbitrary point on the circle. The counter-clockwise angle to the radius at this point as measured from the positivex-axis is the angle . Thex-coordinate of this point is . To add radians to this angle, go to the point on the opposite side of the circle, on the other end of the diameter. Can you see what relation the newx-coordinate will always have with the original?