Section Summary: 3.5

  1. Definitions

    Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.

    You should know the definitions of the various ``secondary'' trig functions, which are defined in terms of tex2html_wrap_inline160 and tex2html_wrap_inline162 :

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    displaymath134

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  2. Theorems

    Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.

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    This makes sense graphically, since if we zoom in on the function tex2html_wrap_inline164 as tex2html_wrap_inline166 , 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 tex2html_wrap_inline166 .

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    displaymath141

    displaymath142

    displaymath143

  3. Properties/Tricks/Hints/Etc.

    Make a note of any especially useful properties, tricks, hints, or other materials.

    Identity:

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    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

    Summarize the section in two or three sentences.

    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.





LONG ANDREW E
Mon Feb 5 09:16:03 EST 2001