Domain, range and sign

From the definition as coordinates of a point of the unit circle one reads off at once the domain, range and sign of the three functions.

Property — Domain, range, sign

• $\sin\alpha$ and $\cos\alpha$ are defined for every $\alpha\in\mathbb{R}$, with range $[-1;1]$.
• $\tan\alpha$ is defined for $\alpha\ne \tfrac{\pi}{2}+k\pi$, $k\in\mathbb{Z}$ (where $\cos\alpha = 0$), and its range is the whole of $\mathbb{R}$.
• The signs of $\sin,\cos,\tan$ in the four quadrants are:

	I	II	III	IV
$\sin$	$+$	$+$	$-$	$-$
$\cos$	$+$	$-$	$-$	$+$
$\tan$	$+$	$-$	$+$	$-$

Links

Topics: Trigonometry
Concepts: Cosine · Domain · Range · Sine · Tangent
Functions: Cosine · Sine · Tangent
Skills: Reasoning by cases