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]);