Derivatives of Sine and Cosine
Graphically
We can understand the derivatives of the sine and cosine
functions
both algebraically and graphically. In the first video we take a
graphic look:
Algebraically
To get the derivatives algebraically, we need the two limits we
derived earlier:
limx→0sin(x)x=1andlimx→0cos(x)−1x=0,
as well as the trig addition identities: sin(A+B)=sin(A)cos(B)+cos(A)sin(B),cos(A+B)=cos(A)cos(B)−sin(A)sin(B).
To summarize, we found that
ddxsin(x)=cos(x),andddxcos(x)=−sin(x). |
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