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Math Help - Which of the following is not defined?

  1. #1
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    Question Which of the following is not defined?

    Arcsin(1/9)
    Arccos(-4/3)
    Arctan(11/12)
    Arccot(-4)
    Arcsec(3Pi)

    What exactly is to define a function?
    NOw the answer to this is supposed to be Arccos(-4/3) because -1\leq cos(x) \leq+1

    Is Cos(x) between -1 and +1 because it is DEFINED that way?

    What about arcsec(3Pi)? Is that defined? Isn't arcsec 3Pi = 1/(arccos 3Pi)? and again isn't 3Pi greater than 1 thereby rendering it undefined because -1\leq cos(x) \leq+1

    ?????
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  2. #2
    Member pflo's Avatar
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    Quote Originally Posted by Utterconfusion View Post
    Arcsin(1/9)
    Arccos(-4/3)
    Arctan(11/12)
    Arccot(-4)
    Arcsec(3Pi)

    What exactly is to define a function?
    NOw the answer to this is supposed to be Arccos(-4/3) because -1\leq cos(x) \leq+1

    Is Cos(x) between -1 and +1 because it is DEFINED that way?

    What about arcsec(3Pi)? Is that defined? Isn't arcsec 3Pi = 1/(arccos 3Pi)? and again isn't 3Pi greater than 1 thereby rendering it undefined because -1\leq cos(x) \leq+1

    ?????
    You are confusing the reciprocal function with the inverse function:

    sec(x)=\frac{1}{cos(x)} and \theta = arccos(x)

    Actually, if you work it out you will find that arcsec(x) = arccos(\frac{1}{x}) and not \frac{1}{arccos(x)}

    This means that arcsec(3\pi) = arccos(\frac{1}{3\pi})

    arcsec is defined everywhere EXCEPT between -1 and 1.
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