Derivatives of sine and cosine
Triangle PDQ is congruence to triangle PSR with PR equal to unity.[br]Drag Q or P to approach each other and examine the congruence of the green and brown triangles.[br]What is the orientational relationship between the segments OP and PR?
Consider the graph is a complex plane.[br]The applet shows that the derivative of a unit complex number P with respect to its argument.[br]The derivative is equal to P rotated anti-clockwise by a right angle.[br]Hence, [math]\frac{dP}{d\theta}=iP[/math]. Solving for P to yield [math]P=e^{i\theta}[/math].