Question

Which of the following trigonometric functions has a range of all real numbers? Select all that apply.

y = sin x
y = cos x
y = tan x
y = cot x
y = csc x
y = sec x

Answer 1

 y = tan x
y = cot x
this is the answer 

Answer 2

Answer:

$\tan x$ and $\cot x$

Step-by-step explanation:

Range of the set of output values.

Range o trigonometric functions are shown below:

Function            Range

$\sin x$             $[-1,1]$

$\cos x$             $[-1,1]$

$\tan x$             All real numbers

$\cot x$             All real numbers

$\sec x$             $(-\infty,-1]\cup [1,\infty)$

$\csc x$             $(-\infty,-1]\cup [1,\infty)$

We need to find the trigonometric functions that has a range of all real numbers.

Therefore, range of $\tan x$ and $\cot x$ functions is all real numbers.