A review of the basic properties of trigonometric functions may be found at http:\/\/fc\/lc\/functions\/trig\/main.html<\/a> The homework consists of the five problems from the Calculus book,<\/p>\n page 383: 4, 17, 19, 23, 33 and the following two problems:<\/em> 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 5PM 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…<\/p>\n
\nThe homework is due by 5PM on Monday, September 13. It may be turned in either to me or to the slot on the wall outside my office (G215-A).<\/p>\n
\nRead each problem completely before attempting the problem<\/span>
\n6.<\/b> Sketch a graph of the function f(x<\/i>)=arctan(x<\/i>)+arccot(x<\/i>). Be sure to label all important values. Explain why the graph has this form. (If you try to use Maple<\/i> to plot this function, be sure to include a range in the plot<\/tt> command. If you forget to do so, then remember that Ctrl-Alt-Del will stop the Maple<\/i> session if you click on the “End Task” option.) d
\n7.<\/b> Let g(x<\/i>)=cos(x<\/i>)*cos(2x<\/i>)*cos(3x<\/i>).
\n(A) Determine all values of x<\/i> between 0 and Pi (inclusive) for which g(x<\/i>)=1\/8.
\n(B) Determine all values of x<\/i> between 0 and 2*Pi (inclusive) for which g(x<\/i>)=1\/8.
\nExtra Thought Exercise<\/i> (does not count as part of the 10 points):
\nLet g(x)=cos(x<\/i>)*cos(2x<\/i>)*cos(3x<\/i>). Determine all values of x<\/i> for which g(x<\/i>)=1\/8. (hint: Answers in terms of Pi might be instructive)
\nExplain why these are the values where g(x<\/i>)=1\/8 and why there are no other values.<\/p>\n
\n\n