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Math Help - Sec, cot, csc

  1. #1
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    Sec, cot, csc

    What does sec, cot and csc stand for in Trig. When you are trying to find something in degrees and pi wise. Like

    sec (30 degrees) * cot (45 degress

    sec `pi - csc (`pi/2)

    Is there a certain number that sec, cot, and csc stand for like sin, cos, and tan?
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  2. #2
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    You should have definitions:

    sec(x) = 1/cos(x)

    csc(x) = 1/sin(x)

    cot(x) = 1/tan(x)
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    Quote Originally Posted by christenc05 View Post
    What does sec, cot and csc stand for in Trig. When you are trying to find something in degrees and pi wise. Like

    sec (30 degrees) * cot (45 degress

    sec `pi - csc (`pi/2)

    Is there a certain number that sec, cot, and csc stand for like sin, cos, and tan?
    What are they:
    They are reciprocal for \sin x, \cos x, \tan x.

    \mathrm{sec}x = \frac{1}{\cos x}, \mathrm{csc}x=\frac{1}{\sin x}, \mathrm{cot}x = \frac{1}{\tan x}.


    Calculation:
    You can change it in terms of \sin x, \cos x, \tan x and work with them.

    Question 1:
    \sec(30^\circ) * \cot(45^\circ)
    = \frac{1}{\cos(30^\circ)} *  \frac{1}{\tan(45^\circ)}
    =\frac{1}{\frac{\sqrt{3}}{2}} * \frac{1}{1}
    =\frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}

    Question 2:
    \sec\left(\pi\right) - \csc \left(\frac{\pi}{2}\right)
    \frac{1}{\cos \left(\pi\right)} - \frac{1}{\sin \left(\frac{\pi}{2}\right)}
    =\frac{1}{-1} - \frac{1}{1}
    =-2
    Last edited by Simplicity; June 20th 2008 at 12:25 PM.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Air View Post
    What are they:
    They are {\color{red}inverse} for \sin x, \cos x, \tan x.
    Careful here, would you like to restate that maybe?
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  5. #5
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    Quote Originally Posted by Mathstud28 View Post
    Careful here, would you like to restate that maybe?
    Hmm...Help me with the wording. I mean that it's 1 over the function.

    EDIT: Got it, it's the reciprocal.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Air View Post
    Hmm...Help me with the wording. I mean that it's 1 over the function.
    They are not inverse functions, they are reciprocals of the normal trigonometric functions.

    Inverse would be like \arccos(x),\arctan(x) etc.

    Thanks for helping though, great working just a little off on the terminology.
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  7. #7
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    They are not inverse functions, they are reciprocals of the normal trigonometric functions.

    Inverse would be like \arccos(x),\arctan(x) etc.

    Thanks for helping though, great working just a little off on the terminology.
    Lol ! That's funny, in France it's exactly the inverse opposit
    Litterally, inverse would be 1/... and reciprocal would be arctan, etc...
    Pretty confusing !
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    Lol ! That's funny, in France it's exactly the inverse opposit
    Litterally, inverse would be 1/... and reciprocal would be arctan, etc...
    Pretty confusing !
    Yeah, haha, here the same can be said of numbers

    The inverse and reciporcal of some number a are both interpreted as \frac{1}{a}

    Where as in functions the definiton would probably be given by

    Let f(x) be a function, then g(x) is a reciprocal function iff f(x)\cdot{g(x)}=1

    and g(x) is an inverse function iff

    f(g(x))=x
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