Question

Which function has a domain of all real numbers?
A. Y=tanx
B. Y=cosx
C. Y=1/sinx
D. Y= secx

Answer 1

is there a difference between B. and C. that I am not seeing?

Answer 2

I meant Y=1/sinx

Answer 3

ok I am pretty sure the domain of y=cosx continues into infinity in both directions+,- only the range is restricted from 1 to -1

Answer 4

y= tanx has aymptotes. I think y = secx has asymptotes and I also think that y= 1/sinx has asymptotes as well but Im a bit lazy to look them up.

Answer 5

Think of it this way:\[A. y=\tan x = \frac{ \sin x }{ \cos x }\]\[B. y=\cos x\]\[C. y=\frac{ 1 }{ \sin x }\]\[D. y=\sec x = \frac{ 1 }{ \cos x }\]In order for the domain to be the set of all real numbers, there must not exist a real number that would make any denominator equal to zero, as that would lead to an undefined value. Does that help?

Answer 6

So it would be B, y=cosx?

Answer 7

Very good.