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Math Help - Probably a stupid question...

  1. #1
    Member Chokfull's Avatar
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    Probably a stupid question...

    So by the trigonometric identities, \sec \theta = \frac {1} {\cos \theta}, but according to my calculator, \sec 0 = 1.57, and \cos 0 = 1. how can this be, seeing as \frac {1} {1} = 1.57 isnt true??
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  2. #2
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    Quote Originally Posted by Chokfull View Post
    So by the trigonometric identities, \sec \theta = \frac {1} {\cos \theta}, but according to my calculator, \sec 0 = 1.57, and \cos 0 = 1. how can this be, seeing as \frac {1} {1} = 1.57 isnt true??
    When you calculated Sec(0), you didn't happen to find Cos^{-1}(0) by any chance in radian mode?

    Cos^{-1}\theta and \frac{1}{Cos\theta} are different.
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    I think Archie nailed it, also showing at the same time the advantage and disadvantage of the calculator/computer. Interesting how the English language can be so subtle and so frustrating at times: "The inverse function" and the inverse OF a function."
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  4. #4
    Member Chokfull's Avatar
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    OK yes i did find \cos ^{-1} (0) on my calculator, because my calculator does not have a secant key. I even searched through all its functions and didn't find it. So I now have 2 more questions:

    (1) how do you find cosecant, secant, and cotangent on a TI-85 graphing calculator, and

    (2) why are \frac {1} {\cos 0} and \cos ^{-1} different?
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  5. #5
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    Quote Originally Posted by Chokfull View Post
    OK yes i did find \cos ^{-1} (0) on my calculator, because my calculator does not have a secant key. I even searched through all its functions and didn't find it. So I now have 2 more questions:

    (1) how do you find cosecant, secant, and cotangent on a TI-85 graphing calculator, and

    (2) why are \frac {1} {\cos 0} and \cos ^{-1} different?
    1. You calculate the sine, cosine, and tangent functions (respectively) and then calculate the multiplicative inverse.

    2. \frac {1} {\cos x} = \sec x but

    \cos ^{-1} (x) = \arccos x, which is the inverse of the cosine function. It tells you the angle that would produce a cosine of x.
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