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$ (\color{blue}{\cos} \: \theta ,\color{red}{\sin}\: \theta) $

Convert 12° to radians with $\pi $ terms.

$$ \int \sin x \: dx$$	$$= - \cos x + C$$	$$\int \arcsin x \: dx $$	$$= x \arcsin x + \sqrt{1-x^{2}} +C \:\:\:\: $$	$$\int \frac{1}{\sqrt{a^{2}-x^{2}}} \: dx $$	$$= \arcsin \frac{x}{a} + C $$
$$ \int \cos x \: dx$$	$$= \sin x $$	$$\int \arccos x \: dx $$	$$= x \arccos x - \sqrt{1-x^{2}} +C $$
$$ \int \tan x \: dx $$	$$= - \ln (\cos x) + C $$	$$ \int \arctan x \:dx $$	$$= x \arctan x - \frac{1}{2} \ln(1+x^{2})+ C \:\:\:\: $$	$$\int \frac{1}{a^{2}+x^{2}} \: dx $$	$$= \frac{1}{a} \arctan \frac{x}{a} +C$$
$$ \int \cot x \: dx$$	$$= \ln (\sin x) + C$$	$$ \int \text{arccot } x \: dx $$	$$= x \text{ arccot }x + \frac{1}{2} \ln(1+x^{2})+ C $$
$$ \int \sec x \: dx$$	$$= \ln ( \sec x + \tan x) + C$$	$$ \int \text{arcsec } x \: dx $$	$$= x \text{ arcsec } x - \ln \left[ x \left( 1+ \frac{x^{2}-1}{x^{2}} \right)\right]+C \:\:\:\: $$	$$\int \frac{1}{x\sqrt{x^{2}-a^{2}}} \:dx $$	$$= \frac{1}{a} \text{arcsec} \frac{x}{a} +C $$
$$ \int \csc x \: dx$$	$$= - \ln( \csc x + \cot x ) +C \:\:\:\: $$	$$\int \text{ arccsc } x \: dx $$	$$= x \text{ arccsc } x + \ln \left[ x \left( 1+ \frac{x^{2}-1}{x^{2}} \right)\right]+C $$
$$ \int \sec^{2} x \: dx$$	$$= \tan x +C $$
$$ \int \csc^{2} x \: dx$$	$$= -\cot x + C$$
$$\int x \cos x \:dx $$	$$= x \sin x + \cos x $$
$$\int x \sin x \:dx $$	$$= - x \cos x + \sin x $$
$$\int x \tan x \:dx $$	$$= \frac{1}{2} i \left( Li ( -e^{2ix}) + x^{2}+ 2ix \ln(1+e^{2ix})\right) $$

Inverse trigonometric functions are the opposite for the function.

Name	Usual notation	Definition	Domain of x for real result	Range of usual principal value (radians)	Range of usual principal value (degrees)
arcsine	$y = \arcsin(x), \: \sin^{-1}$	$x = \sin(y) $	$−1 \leqslant x \leqslant 1 $	$−\frac{\pi}{2} \leqslant y \leqslant \frac{\pi}{2}$	$ −90° \leqslant y \leqslant 90° $
arccosine	$ y = \arccos(x), \: \cos^{-1} $	$ x = \cos(y)$	$−1 \leqslant x \leqslant 1 $	$0 \leqslant y \leqslant \pi $	$0° \leqslant y \leqslant 180° $
arctangent	$y = \arctan(x), \: \tan^{-1}$	$x = \tan(y)$	all real numbers	$−\frac{\pi}{2} < y < \frac{\pi}{2} $	$−90° < y < 90° $
arccotangent	$y = \text{arccot}(x), \: \cot^{-1}$	$x = \cot(y)$	all real numbers	$ 0 < y < \pi$	$0° < y < 180° $
arcsecant	$y = \text{arcsec }(x), \: \sec^{-1}$	$x = \sec(y) $	$ x \leqslant −1 $ or $ 1 \leqslant x $	$ 0 \leqslant y < \frac{\pi}{2} $ or $\frac{\pi}{2} < y \leqslant \pi $	$0° \leqslant y < 90°$ or $ 90° < y \leqslant 180°$
arccosecant	$ y = \text{arccsc}(x), \: \csc^{-1} $	$x = \csc(y)$	$ x \leqslant −1 $ or $ 1 \leqslant x $	$−\frac{\pi}{2} \leqslant y < 0 $ or $ 0 < y \leqslant \frac{\pi}{2} $	$−90° \leqslant y < 0°$ or $ 0° < y \leqslant 90° $

Parent Article: Mathematics

Name	Usual notation	Definition	Domain of x for real result	Range of usual principal value (radians)	Range of usual principal value (degrees)
arcsine	\(y = \arcsin(x), \: \sin^{-1}\)	\(x = \sin(y) \)	\(−1 \leqslant x \leqslant 1 \)	\(−\frac{\pi}{2} \leqslant y \leqslant \frac{\pi}{2}\)	\( −90° \leqslant y \leqslant 90° \)
arccosine	\( y = \arccos(x), \: \cos^{-1} \)	\( x = \cos(y)\)	\(−1 \leqslant x \leqslant 1 \)	\(0 \leqslant y \leqslant \pi \)	\(0° \leqslant y \leqslant 180° \)
arctangent	\(y = \arctan(x), \: \tan^{-1}\)	\(x = \tan(y)\)	all real numbers	\(−\frac{\pi}{2} < y < \frac{\pi}{2} \)	\(−90° < y < 90° \)
arccotangent	\(y = \text{arccot}(x), \: \cot^{-1}\)	\(x = \cot(y)\)	all real numbers	\( 0 < y < \pi\)	\(0° < y < 180° \)
arcsecant	\(y = \text{arcsec }(x), \: \sec^{-1}\)	\(x = \sec(y) \)	\( x \leqslant −1 \) or \( 1 \leqslant x \)	\( 0 \leqslant y < \frac{\pi}{2} \) or \(\frac{\pi}{2} < y \leqslant \pi \)	\(0° \leqslant y < 90°\) or \( 90° < y \leqslant 180°\)
arccosecant	\( y = \text{arccsc}(x), \: \csc^{-1} \)	\(x = \csc(y)\)	\( x \leqslant −1 \) or \( 1 \leqslant x \)	\(−\frac{\pi}{2} \leqslant y < 0 \) or \( 0 < y \leqslant \frac{\pi}{2} \)	\(−90° \leqslant y < 0°\) or \( 0° < y \leqslant 90° \)