Graphing Sin and Cosine Functions
Date: 5/24/96 at 4:22:51 From: Oniga M si Basu C Subject:Graphing Sin and Cosine Functions Hello! I am a pre-college student (18 years) studying Mathematical Analysis. I will have my final exams at the end of June and I really need some help in finding the graphs of the following functions: f:D->R,where D is the maximum domain of definition of each function a) f(x) = pi*x + sin(pi*x), where pi=3.141592654... b) f(x) = (sinx-cosx)/cos(2x) c) f(x) = [tg(3x)]/(tgx*tgx*tgx) OR f(x) = [tan(3x)]/(tanx*tanx*tanx) d) f(x) = (sinx*sinx) - 2(sinx*sinx*sinx*sinx) Also, it will be of real help if you can find all the characteristic elements of the functions. Thank you very much, indeed!
Date: 5/24/96 at 11:3:54 From: Doctor Ethan Subject: Graphing Sin and Cosine Functions Okay, let's get to it: a) f(x) = pi*x + sin(pi*x) The first thing to do is determine the domain. Both x and sin(x) have the same domain and it is all of R so our domain is all of R. Now to go about graphing. To get some idea we can plug in a few points f(0) = 0 + sin(0) = 0 f(pi) = pi^2 + sin(pi) = pi^2 f(2pi) = 2pi^2 + sin(2pi) = 2pi^2 So what we have here is a line of slope pi except that it is moved up or down by a value of sin(x). To graph, I recommend that you lightly draw a line with a slope of pi, marking the points at pi intervals and then draw a tilted sin curve along the line. Next: b) f(x) = (sinx-cosx)/cos(2x) Here the big domain issue is that the denominator can't be zero. So we need to check when does cos(2x) = 0. That is when 2x = (2n+1)pi/2 or x = (2n+1)pi/4. So the domain is all of R except for the points of the form (2n+1)pi/4. Since all of the parts of this equation have a period of pi or less we can just examine the section from 0 to pi. I recommend that you just plug in a bunch of points to see what it looks like. This same strategy will work for c) and d). Why don't you try them out and write back if you need more help. -Doctor Ethan, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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