## anonymous one year ago which function is odd? Check all that apply. a) y=sin(x) b) y=csc(x) c) y=sec(x) d) y=cot(x)

1. anonymous

i know a and b are correct. Idk about c and d

2. anonymous

help

3. anonymous

plz

4. amoodarya

do you know cos(x) is even or odd ?

5. amoodarya

so you can write sec(x)=1/cos(x)

6. anonymous

cos(x) is even.

7. amoodarya

$f(x)=\frac{1}{cosx}\\f(-x)=\frac{1}{\cos(-x)}=\frac{1}{cosx}$ so ?

8. anonymous

@Agl202

9. amoodarya

$cotan(x)=\frac{sinx}{cosx}\\f(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-sinx}{cosx}=-\frac{sinx}{cosx}=-f(x)$

10. Agl202

y = sec x = 1/cos x substitute -x 1/ cos -x =1/cos x = sec x = y -----> even y = sin x substitute -x sin -x = - sin x = -y --------> odd y= cot x = cos x/sin x substitute -x cos -x / sin -x = cos x / (-sin x) = - cot x = -y ---------> odd y = csc x = 1 / sin x substitute -x 1/ sin -x = 1/ (-sin x)=-csc x =-y ----------> odd

11. anonymous

DANG.

12. anonymous

so the only function that is even is cos(x)?

13. Agl202

Ya, So the other three are ur odd ones!

14. anonymous

so the answer is A,B,C,D?

15. amoodarya

note that :sec(x) is even !!!