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2 Problems/Trig Function and Identity

  1. Sep 20, 2009 #1
    Hello everyone. I officially have the worst Trig teacher in America and I have never been so confused in a math class before. I have at least 5 problems (only 2 posted here) I'm struggling with and need to figure out before my exam tomorrow. Any help is much appreciated.

    1.
    1. The problem statement, all variables and given/known data

    The function f(x) = x - sin x is odd. True or False?

    2. Relevant equations



    3. The attempt at a solution

    From my professors review I know it's True but his explanation was so unclear I don't know why. ??


    2.
    1. The problem statement, all variables and given/known data

    sin[tex]\alpha[/tex][tex]/[/tex]1-cos[tex]\alpha[/tex]- sin[tex]\alpha[/tex][tex]/[/tex]1+cos[tex]\alpha[/tex]=


    2. Relevant equations



    3. The attempt at a solution
    I ended up with 0 as the solution. ??
     
    Last edited: Sep 20, 2009
  2. jcsd
  3. Sep 20, 2009 #2
    For a function to be odd, it must satisfy f(-x) = -f(x)
    Try applying that to your function.

    Is this what you mean for the second one?
    [tex]\frac{sin\alpha}{1 - cos\alpha} - \frac{sin\alpha}{1 + cos\alpha}[/tex]

    Are you supposed to simplify it or prove an identity?
     
  4. Sep 20, 2009 #3
    So on the function problem I need to substitute -x and -f into the equation and solve?

    On the identity problem they want to me simplify and yes you have it correct above.
     
  5. Sep 20, 2009 #4
    With your f(x), evaluate f(-x) and see if you get -f(x). If you do, then f(x) is an odd function.

    For the other problem, show what you tried; I don't think it's equal to 0.
     
  6. Sep 20, 2009 #5
    Cool, I was able to get -f(x) on the first one.

    Honestly I feel really stupid on the second one. I don't know where to start other than getting a common denominator and then evaluating? Is that even how it would go?

    That's probably way wrong but that's why I'm here lol...
     
    Last edited: Sep 20, 2009
  7. Sep 20, 2009 #6
    Try multiplying by the conjugates of the denominators to simplify. That's one of the first things you should try doing with trig problems like this.
     
  8. Sep 20, 2009 #7
    trig functions are just functions of numbers like anything else, you shouldn't think that you aren't allowed to take common denominators..et c and everything else.

    for your question, the denominators 1- cos x and 1+cosx, the answer should be fairly clean. And when you get stuck simplifying, keep other known identities in mind (like the Pythagorean theorem).

    The answer isn't 0
     
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