Monkey Rule 5
The fifth monkey rule is about sine and cosine, the two oscillating functions. Thinking back to the chapter about functions, you'll remember that sine was used as the base of the model of the length of the day in Johnson, Vermont. Use our usual code
(x(A),slope(g))
to make some conjectures about the derivative of sine.Indeed, your point B moves long the graph of cosine, and so that means the derivative of sine is cosine. Now let's look at the derivative of cosine. All you have to do is move point A. I've done the rest for you this time.
It's clear that the derivative of cosine, as traced by point B, is not sine. However, it looks like derivative is the mirror image of sine through the x-axis. This means that the derivative of cosine is negative sine.
In summary:
Monkey Rule 5: The derivative of sine is cosine. The derivative of cosine is negative sine.
Move on for the next Monkey Rule!