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Math Help - trig identity problem (sort of)

  1. #1
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    trig identity problem (sort of)

    If tanΘ is undefined and 9pi ≤Θ ≤ 10.265pi ,find sinΘ

    i have tried to solve this and came up with the answer of sinΘ = -1 but this is an incorrect answer according to the answers section in the back of my text book...

    i honestly can't see were i've made a mistake

    please and thank you for your help!
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  2. #2
    A Plied Mathematician
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    If the tangent is undefined, what does that say about the angle \theta? And if you have a restriction on where \theta can be, that should uniquely define the problem.
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  3. #3
    Senior Member eumyang's Avatar
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    I can't either. tan θ is undefined if θ is an odd multiple of pi/2. If tan θ is undefined and 9 pi < θ < 10.265pi, then \theta = \frac{19\pi}{2}, and so \sin \frac{19\pi}{2} = \sin \frac{3\pi}{2} = -1. Is this the complete problem?
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  4. #4
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    i know i still can't find where i made a mistake!

    this is how i approached the problem:

    tan Θ = sin Θ / cos Θ
    and tan Θ can only be undefined if cos Θ = 0

    well, cos Θ = 0 if Θ = 1/2pi + 2npi or 3/2pi + 2npi

    then i found where 9 pi < θ < 10.265 pi which was at θ= 19pi/2

    and i used my calculator to solve sin (19pi/2) to get and answer of -1

    this is the complete problem...

    and thank you to all who helped me!

    a special thanks to eumyang because i never made the connection that tan θ is undefined at odd multiple of pi/2
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