Math 3
Winter 2004
Section 3.5, Derivatives of trigonometric functions
We start by graphing the functions f(x)=sin(x) and g(x)=cos(x).
> | plot(sin(x),x=-Pi..3*Pi); |
> | plot(cos(x),x=-Pi..3*Pi,color=blue); |
Using the interpertation of the derivative as slope of the tangent lines to the graph of the curve, what can you observe
about the two graphs?
Answer: ( sin(x) )' = cos(x) and ( cos(x) )' = - sin(x).
A key computation in proving the above identities is the limit _ =1.
This can be justified by observing that < < 1 and then using Squeeze Theorem.
> | plot([cos(x),1,sin(x)/x],x=-Pi/2..Pi/2,y=0..1.1,color=[green,green,red]); |