   Trigonometric Equations
  I''ve been having a lot of trouble with this one mathematical equation. I know it is silly, but my teacher, the back of the book, and various online sources seem to be in conflict about the answer.The equation is tan 2x = 1 in the domain 0 <= x <= 2pi.I did it the following way:2x = tan-1(1) = 0.782x = pi + 0.78 = 3.92x = 0.78 / 2 = 0.39x = 3.92 / 2 = 1.96So those are my base solutions. Now, I found the period of the function based on the 1/2 compression:pi / k = pi / 2So then, since it is a half-compression, I found the other two solutions:0.39 + pi/2 = 1.961.96 + pi/2 = 3.53So, there are only three solutions? Or am I doing something wrong? 
  I really don''t understand how you are doing that problem, but then again its been a while since I was in Trigonometry. Just by looking at the equation however, my solutions come out to two possibilities, as multiples of pi/8 in the first and third quadrants. ;  lazy way (ie the way I would do it), graph tan(2x) - 1 on a graphing calculator, find zeros. if anything, maybe use it to check what source is right.edit: of course, the zeros between 0 and 2pi.   [edited by - billybob on February 3, 2004 8:53:53 PM];  You already have the first two solutions, so you can add pi/2 to get the third and again to get the fourth. ;  Let me recall my math.tan(2x) = 12x = n(pi) + pi/4, where n is an integerso x = n(pi)/2 + pi/8Is this right? ;  I agree to what Peter19852001 says. ;  Folks,Please do not give a full answer to this homework problem. Just give UBC_Wiskatos hints or suggestions. The post DOES follow forum policy with respect to homework since they showed their work, and basically disclosed that it is schoolwork. (Thank you for that UBC*,  )Forum FAQ Graham RhodesSenior ScientistApplied Research Associates, Inc. ;  HINT - There are four answers in totalTRUST ME i have done a million questions like this. [edited by - jajce85 on February 5, 2004 3:50:36 AM];  If you think about, for whatever ''x'' you give as input, the actual value that tangent operates on is twice that.  This means, that as ''x'' goes from 0 to 2PI, the actual parameter for tangent is going twice as fast.  That means we can squeeze in tangent parameters from 0 to 4PI, which is how we know there are four solutions.  You know what parameter values will cause tangent to evaluate to 1 - simply find the corresponding values of ''x'' that make such parameters. ;quote:Original post by jajce85  HINT - There are four answers in totalTRUST ME i have done a million questions like this.Nice post (though I think the poster already knew there were 4 answers. Hints are great in reply to homework/schoolwork. This kind of teaser reply is the sort of thing that can be thought provoking, which is what drives students to work hard at math! Graham RhodesSenior ScientistApplied Research Associates, Inc. 