The Sign of a Trigonometric Function

The sign of a trigonometric functional value of an angle $\theta$ (not quadrantal) can be easily determined from the quadrant in which the terminal side of $\theta$ lies, as summarized in the following table. The table considers only one revolution of the terminal side of $\theta$ around the unit circle (i.e. from 0 to $2\pi$ radians.) The same applies to integer multiples of $2\pi$ of these angles, since those will be coterminal with these.

$\theta$	Quadrant	$\sin\theta$	$\csc\theta$	$\cos\theta$	$\sec\theta$	$\tan\theta$	$\cot\theta$
$0<\theta<\frac{\pi}{2}$	I	positive	positive	positive	positive	positive	positive
$\frac{\pi}{2}<\theta<\pi$	II	positive	positive	negative	negative	negative	negative
$\pi<\theta<\frac{3\pi}{2}$	III	negative	negative	negative	negative	positive	positive
$\frac{3\pi}{2}<\theta<2\pi$	IV	negative	negative	positive	positive	negative	negative