Template:EqualOrNegativeIdenticalTrigonometricFunctionsSolutions/doc

Usage with no options

Calling

{{DomainsImagesAndPrototypesOfTrigAndInverseTrigFunctions}}

will display:

Name	Symbol		Domain		Image/Range	Inverse function		Domain		Image of principal values
sine	$\sin$	$:$	$\mathbb {R}$	$\to$	$[-1,1]$	$\arcsin$	$:$	$[-1,1]$	$\to$	$\left[-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right]$
cosine	$\cos$	$:$	$\mathbb {R}$	$\to$	$[-1,1]$	$\arccos$	$:$	$[-1,1]$	$\to$	$[0,\pi ]$
tangent	$\tan$	$:$	$\pi \mathbb {Z} +\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$	$\to$	$\mathbb {R}$	$\arctan$	$:$	$\mathbb {R}$	$\to$	$\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$
cotangent	$\cot$	$:$	$\pi \mathbb {Z} +(0,\pi )$	$\to$	$\mathbb {R}$	$\operatorname {arccot}$	$:$	$\mathbb {R}$	$\to$	$(0,\pi )$
secant	$\sec$	$:$	$\pi \mathbb {Z} +\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$	$\to$	$\mathbb {R} \setminus (-1,1)$	$\operatorname {arcsec}$	$:$	$\mathbb {R} \setminus (-1,1)$	$\to$	$[\,0,\;\pi \,]\;\;\;\setminus \left\{{\tfrac {\pi }{2}}\right\}$
cosecant	$\csc$	$:$	$\pi \mathbb {Z} +(0,\pi )$	$\to$	$\mathbb {R} \setminus (-1,1)$	$\operatorname {arccsc}$	$:$	$\mathbb {R} \setminus (-1,1)$	$\to$	$\left[-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right]\setminus \{0\}$

With includeTableDescription

Calling

{{DomainsImagesAndPrototypesOfTrigAndInverseTrigFunctions|includeTableDescription=true}}

will display:

The table below displays names and domains of the inverse trigonometric functions along with the range of their usual principal values in radians.

Name	Symbol		Domain		Image/Range	Inverse function		Domain		Image of principal values
sine	$\sin$	$:$	$\mathbb {R}$	$\to$	$[-1,1]$	$\arcsin$	$:$	$[-1,1]$	$\to$	$\left[-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right]$
cosine	$\cos$	$:$	$\mathbb {R}$	$\to$	$[-1,1]$	$\arccos$	$:$	$[-1,1]$	$\to$	$[0,\pi ]$
tangent	$\tan$	$:$	$\pi \mathbb {Z} +\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$	$\to$	$\mathbb {R}$	$\arctan$	$:$	$\mathbb {R}$	$\to$	$\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$
cotangent	$\cot$	$:$	$\pi \mathbb {Z} +(0,\pi )$	$\to$	$\mathbb {R}$	$\operatorname {arccot}$	$:$	$\mathbb {R}$	$\to$	$(0,\pi )$
secant	$\sec$	$:$	$\pi \mathbb {Z} +\left(-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right)$	$\to$	$\mathbb {R} \setminus (-1,1)$	$\operatorname {arcsec}$	$:$	$\mathbb {R} \setminus (-1,1)$	$\to$	$[\,0,\;\pi \,]\;\;\;\setminus \left\{{\tfrac {\pi }{2}}\right\}$
cosecant	$\csc$	$:$	$\pi \mathbb {Z} +(0,\pi )$	$\to$	$\mathbb {R} \setminus (-1,1)$	$\operatorname {arccsc}$	$:$	$\mathbb {R} \setminus (-1,1)$	$\to$	$\left[-{\tfrac {\pi }{2}},{\tfrac {\pi }{2}}\right]\setminus \{0\}$