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Math Help - Finding numbers which satisfy trigonometric equations

  1. #1
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    Finding numbers which satisfy trigonometric equations

    This is the question:

    Find the numbers(s) x in the interval [0, 2Pi] which satisfies the equation,
    tan x / 2 = 1

    I multiplied both sides by 2, and solved for x using my calculator:
    tan x = 2
    x = 63.43

    However, the answer is Pi/2. What have I done wrong? 63.43 degrees is a long shot from 90 degrees. :/
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by Glitch View Post
    This is the question:

    Find the numbers(s) x in the interval [0, 2Pi] which satisfies the equation,
    tan x / 2 = 1

    I multiplied both sides by 2, and solved for x using my calculator:
    tan x = 2
    x = 63.43

    However, the answer is Pi/2. What have I done wrong? 63.43 degrees is a long shot from 90 degrees. :/
    tan\frac{x}{2} \neq \frac{1}{2}tan{x} (edit: it equals only at x=2\pi n


    Anyway....

    Hint:

    When sinx and cosx get the same values, and way solving my hint answer your question?
    Last edited by Also sprach Zarathustra; July 12th 2010 at 07:44 AM.
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  3. #3
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    Quote Originally Posted by Glitch View Post
    This is the question:

    Find the numbers(s) x in the interval [0, 2Pi] which satisfies the equation,
    tan x / 2 = 1

    I multiplied both sides by 2, and solved for x using my calculator:
    tan x = 2
    x = 63.43

    However, the answer is Pi/2. What have I done wrong? 63.43 degrees is a long shot from 90 degrees. :/
    Are you sure it's not

    \tan{\left(\frac{x}{2}\right)} = 1?

    If so, you should get

    \frac{x}{2} = \tan^{-1}(1)

    \frac{x}{2} = \frac{\pi}{4} + \pi n where n \in \mathbf{Z}

    x = \frac{\pi}{2} + 2\pi n.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    Are you sure it's not

    \tan{\left(\frac{x}{2}\right)} = 1?
    Ahh, that may be it. The textbook wrote it exactly how I did in my first post (which isn't very clear). Thank you.
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