JHR's IFYCSEM notes for 9/9/99

Trigonometric functions and their inverses

A review of the basic properties of trigonometric functions may be found at http://fc/lc/functions/trig/main.html
The homework is due by 5 PM on Monday, September 13. It may be turned in either to me or to the slot on the wall outside my office (G215-A).

The homework consists of the five problems from the Calculus book,
page 383: 4,17,19,23,33 and the following two problems;
Read each problem completely before attempting the problem
6. Sketch a graph of the function f(x)=arctan(x)+arccot(x). Be sure to label all important values. Explain why the graph has this form. (If you try to use Maple to plot this function, be sure to include a range in the plot command. If you forget to do so, then remember that Ctrl-Alt-Del will stop the Maple session if you click on the "End Task" option.)
7. Let g(x)=cos(x)*cos(2x)*cos(3x).
(A) Determine all values of x between 0 and Pi (inclusive) for which g(x)=1/8.
(B) Determine all values of x between 0 and 2*Pi (inclusive) for which g(x)=1/8.
Extra Thought Exercise (does not count as part of the 10 points):
Let g(x)=cos(x)*cos(2x)*cos(3x). Determine all values of x for which g(x)=1/8. (hint: Answers in terms of Pi might be instructive)
Explain why these are the values where g(x)=1/8 and why there are no other values.