The trigonometric functions that have a range of all real numbers are:
- \( y = \tan x \)
- \( y = \cot x \)
Both the tangent and cotangent functions can take any real value as \( x \) varies, hence their ranges are all real numbers.
The other functions listed (sine, cosine, cosecant, and secant) have limited ranges:
- \( y = \sin x \) has a range of \([-1, 1]\).
- \( y = \cos x \) has a range of \([-1, 1]\).
- \( y = \csc x \) has a range of \((-\infty, -1] \cup [1, \infty)\).
- \( y = \sec x \) has a range of \((-\infty, -1] \cup [1, \infty)\).
Therefore, the correct answers are:
- \( y = \tan x \)
- \( y = \cot x \)