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Math Help - Inverse cotangent on calculator.

  1. #1
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    Inverse cotangent on calculator.

    Hello. This should be an easy one, but the answer I'm getting doesn't match the answer in my text book, so I just want someone to help me either confirm it as a misprint or show me what I did wrong:

    The question is:

    Evaluate the following with a calculator, give the answer in degrees rounded to two decimal places:

    cot^{-1}(-4.2319)

    I get: -13.30 degrees

    My text book says: 166.70 degrees

    Thanks!
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  2. #2
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    for angles in degrees ...

    \cot^{-1}(x) = 90^\circ -\tan^{-1}(x)
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  3. #3
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    On my calculator, I entered: tan^{-1}(1/-4.2319)

    This works for solving many other problems of this type... can someone explain why this is an exception?
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  4. #4
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    For instance, if the problem were:

    csc^{-1}(-3.7893)

    I could enter on my calculator:

    sin^{-1}(1/-3.7893)

    And arrive at the correct answer: -15.30

    Why does this apparently work for inverse cosecant but not inverse cotangent?
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  5. #5
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    Quote Originally Posted by JennyFlowers View Post
    For instance, if the problem were:

    csc^{-1}(-3.7893)

    I could enter on my calculator:

    sin^{-1}(1/-3.7893)

    And arrive at the correct answer: -15.30

    Why does this apparently work for inverse cosecant but not inverse cotangent?
    the ranges of these two inverses don't match up ...

    range of inverse cotangent is from (0,\pi) ... (0^\circ, 180^\circ) , quads I and II

    range of inverse tangent is \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) ... (-90^\circ,90^\circ) , quads I and IV
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  6. #6
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    Thank you!

    Thanks so much!
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