Which function is odd? check all that apply.
a. y = sec x
b. y = sin x
c. y = cot x
d. y = csc x

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

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