Section Summary: 3.5

1. Definitions

   You should know the definitions of the various ``secondary'' trig functions, which are defined in terms of and :

   

   

   

   

2. Theorems

   

   This makes sense graphically, since if we zoom in on the function as , it appears more and more like the line y=x. Thus the ratio should be approaching 1, since they're getting more and more similar as .

   

   

   

   

   

   

   

3. Properties/Tricks/Hints/Etc.

   Identity:

   

   

   This identity comes from the Appendix D, which you may want to consult if you're a little shaky on your trig functions.

   The author notes that the derivatives of the ``co'' functions are the ones with the negative signs.

4. Summary

   In this case we use a few tricks and identities to find the derivative functions for the trigonometric functions. Since all these functions are defined in terms of sines and cosines, if we know the derivatives for these the others can be derived using the quotient rule.

Problems:

Problems pp. 175-177, #4, 10, 13, 24, 26, 31, 35, 40, 45, 46.

On the board: 5, 23, 30, 32.