Write the range of the following trigonometric function:

$cosecx$

Find the range of the following function:

$f\left(x\right)=2-3\cos x$

Find the range of the following  function:

$f\left(x\right)=2+5\sin 3x$

In which quadrant does $x$ lie if $\cos x$ is positive and $\tan x$ is negative.

[Enter numerical value]

In which quadrant does $x$ lie if both $\sin x$ and $\cos x$ are negative.

[Enter numerical value]

In which quadrant does $x$ lie if $\sin x=\frac{4}{5}$ and $\cos x=-\frac{3}{5}$.

[Enter numerical value]