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Odd and even functions, recangular coordinates

  1. Aug 5, 2009 #1
    1.if f and g are odd and even functions , respectively, such that f(a)= b and g(c) = b, b cannot equal 0,
    then [f(-a)/g(-c)] + f(-a) - g(-c) =

    A. -1
    B. -1-2b
    C. -1+2b
    D. 1-2b
    E. 1+2b

    2.if r= 4 sin(angle) is converted to rectangular coordinates , then
    A. x^2 + (y-2)^2 = 4
    B. (x-2)^2 + y^2 = 4
    C. x^2 +y^2 = 16
    D. x^2 +4y^2 = 4
    E (x-2)^2 + (y-2)^2 = 4

    3.




    i don't know how to solve number 1, i'm not sure my solution for number 2



    i don't get number 1
    number 2: i saw a problem like the question is r=4cos(angle) and solution is
    (x-2)^2 + y^2 = 2 , so i guessed A is solution for number 2, please help me.
     
  2. jcsd
  3. Aug 5, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    You aren't going to get very far guessing at all the answers. For 1) look up the definition of odd and even and figure out what f(-a) and g(-c) might be in relation to b. For 2) multiply both sides by r and then look up some standard formulas for conversion between polar and rectangular. You have to show some effort here beyond just guessing.
     
  4. Aug 6, 2009 #3
    I agree that go back to the definition of odd and even function will be helpful.
    f(x)=-f(-x) and g(x)=g(-x),so f(-a)=-b, g(-c)=g(c)=b
    Now,I'm sure you know how to solve it
     
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