Question

Which function is odd? Check all that apply.A. y = sec xB. y = sin xC. y = cot xD. y = csc x

Answer 1

ODD Function : a function such that f (−x) =−f (x) where the sign is reversed but the absolute value remains the same if the sign of the independent variable is reversed.

A) y = secx

Put x = -x

then y = 1/cosx

y = 1/cos(-x)

y = 1/cosx

y = secx

Thus, secx is the even function

B) y = sinx

SUbstitute x = -x

y = sin(-x)

y = -sinx

Thus, y = sinx is the odd function

C) y = cotx

Put x = -x

then y = cot(-x)

y = -cotx

Thus, y = cotx is the odd function

D) y = cscx

Put x = -x

Then. y = csc(-x)

y = -cscx

Answer :

B. y = sin x

C. y = cot x

D. y = csc x​