Derivatives of sine and cosine

Victor Hui
Triangle PDQ is congruence to triangle PSR with PR equal to unity. Drag Q or P to approach each other and examine the congruence of the green and brown triangles. What is the orientational relationship between the segments OP and PR?
Consider the graph is a complex plane. The applet shows that the derivative of a unit complex number P with respect to its argument. The derivative is equal to P rotated anti-clockwise by a right angle. Hence, . Solving for P to yield .