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Math Help - i need trig help - even/odd properties

  1. #1
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    i need trig help - even/odd properties

    ok i dont understand this:

    "which of the following trigonometric values are NEGATIVE?"

    I. sin(-292)
    II. tan(-193)
    III. cos(-207)
    IV. cot222

    ok i have the answer key and apparently it's II and III

    but i thought it was I and II

    in my math book it says cos(-Θ) = cosΘ

    so how the heck is III negative????


    ok is this answer key wrong b/c that makes *no sense*!!!!!
    Last edited by topsquark; June 14th 2008 at 02:16 PM.
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by tangerine_tomato View Post
    ok i dont understand this:

    "which of the following trigonometric values are NEGATIVE?"

    I. sin(-292)
    II. tan(-193)
    III. cos(-207)
    IV. cot222

    ok i have the answer key and apparently it's II and III

    but i thought it was I and II

    wtf??????? in my math book it says cos(-Θ) = cosΘ

    so how the heck is III negative????


    ok is this answer key wrong b/c that makes *no sense*!!!!!
    [tex]\cos(-\theta)=\cos(\theta)[/Math]

    \sin(-\theta)=-\sin(\theta)

    193, 207 and 222 are in the 3rd quadrant, that is to say negative cosine and negative sine.
    292 is in the 4th quadrant, that is to say positive cosine and negative sine.


    For example III, where you seem to have problems.

    \cos(-207)=\cos(207)<0
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,



    \cos(-\theta)=\cos(\theta)

    \sin(-\theta)=-\sin(\theta)

    193, 207 and 222 are in the 3rd quadrant, that is to say negative cosine and negative sine.
    292 is in the 4th quadrant, that is to say positive cosine and negative sine.


    For example III, where you seem to have problems.

    \cos(-207)=\cos(207)<0
    ohhh ok i think get it now...so i just have to see what quadrant each is in??? AND look at the even odd properties???
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  4. #4
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    Quote Originally Posted by tangerine_tomato View Post
    ohhh ok i think get it now...so i just have to see what quadrant each is in??? AND look at the even odd properties???
    You don't have to worry about even/odd, but it may be helpful. What you do need to realize is that you are being asked when the function is negative, not when the function's argument is negative. Thus, 270^\circ is certainly positive, but its sine is negative since \sin270^\circ = -1.

    For example, let's look at \tan\left(-193^\circ\right). Just because the 193 is negative doesn't mean the tangent will be. We need to look at the quadrant. Since this is a negative angle, we move clockwise from the x-axis. Go around 193 degrees, and you should see that the angle lies in quadrant II:

    Code:
                    -270
              QUAD    |
               II     |
          ***         |    QUAD I
             ***      |
                ***   |
                   ***|
    -180 ------------+-------------- 0
                      |
                      |
            QUAD III  |   QUAD IV
                      |
                      |
                      |
                    -90
    So, since \sin\left(-193^\circ\right) > 0 and \cos\left(-193^\circ < 0\right), we have

    \tan\left(-193^\circ\right) = \frac{\sin\left(-193^\circ\right)}{\cos\left(-193^\circ\right)} < 0

    Or, you could use the fact that tangent is odd, so \tan\left(-193^\circ\right) = -\tan193^\circ, and since 193^\circ is in quadrant III, the tangent will be positive, and then the negative in front makes it negative. Either method works.
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  5. #5
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    ok that really confuses me

    but i just devised this method of doing problems like that...lol

    1. rewrite it using even-odd properties
    2. draw a picture to see what quadrant it's in
    3. apply the "all students take classes" rule
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