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Math Help - Function value + - or undefined

  1. #1
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    Function value + - or undefined

    Determine whether the function value is positive, negative, zero or undefined.

    tan 25 degree = my answer = positive?
    cot Pi = how do you get this?
    cos -2pi/5 = negative?
    sin -pi/2 = negative?
    csc 0 = how do you get this?



    Also I have a issue with another part of the worksheet, it says determine the quadrant the pheta terminates...

    how do i get this?

    a couple of the problems are
    1.) 6 radians
    2.) cos pheta <0, sin pheta <0

    how do you solve those?
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  2. #2
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    tan (25 degrees) is positive and sin (-pi/2) is negative.

    For cos (-2pi/5), remember cos (-2pi/5) = cos (2pi/5).

    To calculate cot pi, cot x = 1/(tan x).

    To calculate csc 0, csc x = 1/(sin x).
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  3. #3
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    huh? why is the cos positive?
    and i still dont understand the cot or csc
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  4. #4
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    Wait so cot would be pi/(tan pi) = 0
    and csc would be 0/(sin 0) = 0
    ???
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  5. #5
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    The cos is positive because \frac{-2\pi}{5} is in the fourth quadrant, where x is positive, and hence the cos is positive. Or you can use the identity I used, which is cos(-x) = cos x.

    For the other two problems, I used identities again. Can you calculate \frac{1}{\tan \pi} and \frac{1}{\sin 0}?

    Edit: the identities are \cot x = \frac{1}{\tan x} and \csc x = \frac{1}{\sin x}.
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  6. #6
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    so cot pi = 1/ tan pi = 1 / 0 = 0
    and csc 0 = 1/ sin 0 = 1 / 0 = 0?

    would it always be a 1 at the top is that like the equation for cot and csc?
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  7. #7
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    Quote Originally Posted by cokeclassic View Post
    would it always be a 1 at the top is that like the equation for cot and csc?
    For those two identities, yes.

    Also, 1/0 is undefined.
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  8. #8
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    Ok, so how would you know which number goes on the top?
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  9. #9
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    Quote Originally Posted by cokeclassic View Post
    Ok, so how would you know which number goes on the top?
    Just remember

    \sec x = \frac{1}{\cos x}

    \csc x = \frac{1}{\sin x}

    \cot x = \frac{1}{\tan x}

    for all x.
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  10. #10
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    thanks!
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