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

Answer: y= cos x

y=sec x

Explanation:

Answer 2

To know if the function is odd or even, we have to substitute x with -x. If the function remains positive, that would mean the function is even. If the function is negative then the function is odd.

A. y = sec(x) is also equal to 1/cos(x). Substitute x with -x
1/cos(-x) =1/cos(x) = sec(x) = y (EVEN)

B. y = sin(x) Substitute x with -x
sin(-x) = -sin(x) = -y (ODD)

C. y= cot(x) is also equivalent to cos(x)/sin(x) Substitute x with -x
cos(-x) / sin(-x) = cos(x)/ (-sin (x)) = - cot(x) = -y (ODD)

D. y = csc(x) is also equivalent to 1 / sin(x) Substitute x with -x
1/ sin(-x) = 1/ (-sin (x))=-csc(x) =-y (ODD) ----------> odd