Odd and even functions, recangular coordinates

[Tiome_nguyen]

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.

 

[Dick]

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.

 

[Zhujiao]

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