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

`\tan x` and
`\cot x`

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.