Derivatives of sine and cosine

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?

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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, $\frac{dP}{d\theta}=iP$. Solving for P to yield $P=e^{i\theta}$.

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