Question

Which function is odd? Check all that apply.

A. y = sec x
B. y = sin x
C. y = cot x
D. y = csc x

Answer 1

an odd function is a function which when x is substituted with -x, the function is equal to the negative counterpart of the original function. we use pi as x in the expressions

1. y = sec x y = 1/ cos pi/3 = 2
y = 1/ cos -pi = 2
2. y = sin pi/3 = sqrt 3 over 2
y = sin -pi/3 = -sqrt 3 over 2
3. y = 1/ tan pi /3 = sqrt 3 / 3
y = 1/ tan pi /3 = -sqrt 3 / 3
4. y = csc x = 1/ sin pi/3 = 2/sqrt 3
y = csc x = 1/ sin -pi/3 = -2/sqrt 3

odd functions are B, C and D

Answer 2


`The\ function\ is\ odd\ if\ f(-x)=-f(x)\\\\We\ know:\\\sin x;\ \tan x\ and\ \cot x\ are\ odds.\\\cos x\ is\ even\ /\cos(-x)=\cos x/\\--------------------\\\\A.\ y=\sec x\\\\\sec(-x)=(1)/(\cos(-x))=(1)/(\cos x)=\sec x-\fbox {NO}\\\\B.\ y=\sin x-\fbox{YES}\\\\C.\ y=\cot x\\\\\cot(-x)=(\cos(-x))/(\sin(-x))=(\cos x)/(-\sin x)=-(\cos x)/(\sin x)=-\cot x-\fbox{YES}\\\\D.\ y=\csc x\\\\\csc(-x)=(1)/(\sin(-x))=(1)/(-\sin x)=-(1)/(\sin x)=-\csc x-\fbox{YES}`