1. Dean Bates P.3 11-7-2009

2. derivatives of trig functions

3. Basic Problems derivative sin(x) = cos(x) derivative cos(x) = -sin(x) derivative csc(x) = -csc(x)cot(x) derivative sec(x) = sec(x)tan(x) derivative tan(x) = sec 2 (x) derivative cot(x) =-csc 2 (x) NOTE: derivatives of sin, sec and tan are positive; derivatives of cos, csc and cot are negative

4. More Complex Problems “derivative sin(x) = cos(x)” really means: derivative sin (x) = d(x)cos(x) times the result of the power rule for sin(x), which equals (1)(1)cos(x) or cosx the same is true for the other trig functions So, derivative 3sec(x 2 ) = 6xsec(x 2 )tan(x 2 ), and so on. now for a quiz…

5. Questions 1.y=3sec 2 (x) 2.y=[cos(x)] / x 2 3.y=cot 3 (x) Answers 1.d(x)=3(1)[2sec(x)][sec(x)tan(x)] or 6sec 2 (x)tan(x) 2.d(x) =[-2xsin(x)-xcos(x)]/x 4 or [-2sin(x)-cos(x)] / x 3 3.d(x) =3(1)[csc2(x)][cot2(x)] or 3csc 2 (x)cot 2 (x) Get it? If not, then re-read the previous slide. Still don’t get it? Try Rastafarianism.