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Math Help - I am confused on this problem?

  1. #1
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    I am confused on this problem?

    Where did I go wrong on this problem,
    Find the exact value of the expression cos^-1[cos(4PI/3)]

    cos of 4PI/3 =-1/2
    cos^-1 of (-1/2)= 2PI/3 or 2.094395102
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  2. #2
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    Talking

    Last edited by stapel; April 11th 2009 at 12:54 PM. Reason: Better reply follows. Thank you, skeeter!
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  3. #3
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    Quote Originally Posted by cross1933 View Post
    Where did I go wrong on this problem,
    Find the exact value of the expression cos^-1[cos(4PI/3)]

    cos of 4PI/3 =-1/2
    cos^-1 of (-1/2)= 2PI/3 or 2.094395102
    who said it was wrong?

    \cos^{-1}\left[\cos\left(\frac{4\pi}{3}\right)\right] = \cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}

    because ... the range of the inverse cosine function is 0 \leq y \leq \pi
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  4. #4
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    Quote Originally Posted by skeeter View Post
    who said it was wrong?

    \cos^{-1}\left[\cos\left(\frac{4\pi}{3}\right)\right] = \cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}

    because ... the range of the inverse cosine function is 0 \leq y \leq \pi
    2PI/3 is not one of the answer choices, that is what is confusing me.
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  5. #5
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    Quote Originally Posted by stapel View Post
    Domain 1,-1
    Range 0, PI
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  6. #6
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    Quote Originally Posted by cross1933 View Post
    2PI/3 is not one of the answer choices, that is what is confusing me.
    don't know what to tell you ... but, I know my solution is correct.
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  7. #7
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    Quote Originally Posted by skeeter View Post
    don't know what to tell you ... but, I know my solution is correct.
    Not sure what I will do, maybe I will email one of the class members.

    Thanks
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  8. #8
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    for the record, what are the answer "choices" ?
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  9. #9
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    Quote Originally Posted by skeeter View Post
    for the record, what are the answer "choices" ?
    1/2
    -1/2
    pi/3
    4pi/3
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  10. #10
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    Quote Originally Posted by cross1933 View Post
    1/2
    -1/2
    pi/3
    4pi/3
    None of those options are correct. The answer given by you and skeeter is the correct answer.
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  11. #11
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    Is it possible the cos^-1 and the cos cancel leaving the answer as 4PI/3?
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  12. #12
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    Quote Originally Posted by cross1933 View Post
    Is it possible the cos^-1 and the cos cancel leaving the answer as 4PI/3?
    You know that \frac{4 \pi}{3} does not lie in the range of \cos^{-1}, so it cannot be the correct answer. (However, whoever wrote the question might not realise this .....)
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  13. #13
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    Quote Originally Posted by mr fantastic View Post
    You know that \frac{4 \pi}{3} does not lie in the range of \cos^{-1}, so it cannot be the correct answer. (However, whoever wrote the question might not realise this .....)
    That is true, still hoping I overlooked something simple. The author of the question may not be aware of this?
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