cos(x)and for the cosine curve at x it is
We start from
x, and then move a little bit
h. Using the rule for sum of sines (here):
The first term is
(1/h)(1 - cos(h)); last time we showed that
(1/h)(1 - cos(h))equals zero in the limit as
h -> 0.
The second term is
(1/h) sin(h); we showed that
h -> 0. Thus,
Since sine and cosine are periodic with cosine "ahead"