Expert: Vineeth Venugopal - 1/26/2009

Question
Hi, I don't really understand how to do this question.
Find all values of x in the interval [0, 2pi] that satisfy the equation:
|tanx| = 1
(^ absolute value)
I do not understand the absolute value part.. does it make any difference in the values when tanx = 1?

Answer
hi

   The absoluter value or "mod" function actually clubs together two equations into one.
               tanx=1 and tanx=-1.
In either case the |tanx|=1 and hence our original equation is satisfied.
Taking them one by one,
               tanx=1 -> tanx=tan(pi/4)
The period of tan being pi, the general solution is
                 x = (Pi/4)+/-(nPi)
Taking the second equation,
                 tanx=-1,
x being in [0,2pi],  tanx = tan(3pi/4)
                  x = (3Pi/4)+/-(nPi)

 Now since x is kept is [0,2pi], only those values of n that fall in this interval is to taken as the solution.