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Math Help - Graphing Trig Functions

  1. #1
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    Graphing Trig Functions

    Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?
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  2. #2
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    Re: Graphing Trig Functions

    Quote Originally Posted by Manni View Post
    Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?
    Since the tangent and arctangent functions are inverse functions, this is just 2x...
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    Re: Graphing Trig Functions

    Quote Originally Posted by Prove It View Post
    Since the tangent and arctangent functions are inverse functions, this is just 2x...
    not quite. what if x = \frac{\pi}{4}...?

    also, the range of arctan is (-1,1). but we can easily imagine an original input of, oh say 2.

    see for yourself: y = arctan(tan(2x)) - Wolfram|Alpha

    the function is not defined for all real x, and is not even equal to 2x except on (-pi/4,pi/4).
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