Use the fact that the cosine is even and the sine is odd to determine if the following are even, odd, or neither.

Question

anonymous · Answer

$$\cot x$$

anonymous · Answer

@ParthKohli @satellite73

anonymous · Answer

@douglaswinslowcooper

aravindg · Answer

cot x=cos x/sin x

even/odd so odd

anonymous · Answer

How do I show that?

aravindg · Answer

Take an example of x^2 (even) and  and x(odd).

x^2/x=x which is odd

aravindg · Answer

Does that make sense?

anonymous · Answer

ohh okay so with this... does this make sense $$\cot(- x)= \frac{ \cos (-x) }{ \sin (-x) }$$

aravindg · Answer

Yeah that is the actual method.

anonymous · Answer

cot is actually odd...

$\cot x=\Large{\frac{\cos x}{\sin x}}$ so $\cot (-x)=\Large{\frac{\cos (-x)}{\sin (-x)}}=-\Large{\frac{\cos (x)}{\sin (x)}}=-\cot x$

aravindg · Answer

you get cot(-x)=-cot x

anonymous · Answer

WOW! you guys are so helpful! Thanks @AravindG and @pgpilot326 !! Who should I give my medal too!

aravindg · Answer

yw :)

anonymous · Answer

no worries... good luck!

anonymous · Answer

I'll give one, too. I think you can multiply and divide such that even functions are +1 and odd are -1 and the results will be + or - as appropriate. 
cot = cos/sin = (1)/(-1) = -1 thus odd.

anonymous · Answer

thanks @douglaswinslowcooper ! that's another good way.