Let f(x) = -cos(x). Based on the discussion in this section, is a reasonable formula for f'(x)?
Look at the graph of f(x) = -cos(x).
The graph of -cos x looks like this:
We can see where its slope is 0, and where its slope is largest and smallest:
We plot some points on the graph of the derivative:
and play connect the dots to find the graph of sin x: