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Math Help - Trig periods

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    Trig periods

    How do i figure out which period the function is in?
    Im doing the problem 3 tan2 x-1=0
    i got tan x= 1sqrt 3 i have to find a solution to x. How do i know tan is on the interval 0, pi and not 0, 2pi?
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  2. #2
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    Re: Trig periods

    The period of a periodic function f(x) is the smallest positive real number \alpha such that f(x+\alpha)=f(x) for all x in the domain of the function. In case of \tan, \tan(x+\pi)=\tan x for all real x and no positive real number \alpha smaller than \pi satisfies \tan(x+\alpha)=\tan x for all x. (It's true that \tan(x+2\pi)=\tan x for all x but 2\pi is not the smallest such positive real number.)
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    Re: Trig periods

    Quote Originally Posted by noork85 View Post
    How do i figure out which period the function is in?
    Im doing the problem 3 tan2 x-1=0
    i got tan x= 1sqrt 3 i have to find a solution to x. How do i know tan is on the interval 0, pi and not 0, 2pi?
    3\tan^2{x} - 1 = 0

    \tan{x} = \pm \frac{1}{\sqrt{3}}

    since the solution interval is not given, then all possible solutions are ...

    x = \frac{\pi}{6} + k\pi ; k \in \mathbb{Z}

    x = -\frac{\pi}{6} + k\pi ; k \in \mathbb{Z}
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