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Find the values of the following:
$\arcsin 0$
$\textrm{arccot}\, (-\frac{\sqrt{3}}{3})$
$\cot(\textrm{arccot}\,(-3))$
$\cos(\arccos \frac{4}{5})$
$\textrm{arccsc}\, 2$
$\arccos (-1)$
$\csc(\arcsin \frac{3}{5})$
$\textrm{arcsec}\, (\sin \frac{\pi}{2})$
$\sin (\textrm{arcsec}\, 2)$
$\arccos (-\frac{1}{2})$
$\arctan^3 (-\sqrt{3})$
$3\arcsin^2 (\frac{\sqrt{3}}{2})$
$\textrm{arcsec}\, 0$
$\sin(\arctan 2)$
$\arccos(\sin(-\frac{\pi}{6}))$
$\tan(\arccos(-\frac{2}{3}))$
$\arccos 2$
$\cos(\arcsin(-\frac{4}{5}))$
$4 \arctan 1$
$\csc(\textrm{arcsec}\, 12)$
$\textrm{arccsc}\, \sqrt{2}$
$\textrm{arcsec}\, 2$
$\arctan(\sin \frac{\pi}{2})$
$\arctan(\cos \pi)$
$\arcsin (\tan \frac{\pi}{4})$
$0$
$\frac{2\pi}{3}$
$-3$
$\frac{4}{5}$
$\frac{\pi}{6}$
$\pi$
$\frac{5}{3}$
$0$
$\frac{\sqrt{3}}{2}$
$\frac{2\pi}{3}$
$-\frac{\pi^3}{27}$
$\frac{\pi^2}{3}$
no value
$\frac{2}{\sqrt{5}}$
$\frac{2\pi}{3}$
$-\frac{\sqrt{5}}{2}$
no value
$\frac{3}{5}$
$\pi$
$\frac{12}{\sqrt{143}}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$
$\frac{\pi}{4}$
$-\frac{\pi}{4}$
$\frac{\pi}{2}$
Write the given expression in terms of $x$ without any trigonometric functions:
$\sin(\arctan x)$
$\tan(\arcsin x)$
$\cot(\arcsin x)$
$\cos(\arcsin x)$
$\cos(\textrm{arcsec}\, x)$
$\csc(\textrm{arccot}\, \frac{x}{4})$
$\displaystyle{\frac{x}{\sqrt{x^2 + 1}}}$
$\displaystyle{\frac{x}{\sqrt{1-x^2}}}$
$\displaystyle{\frac{\sqrt{1-x^2}}{x}}$
$\displaystyle{\sqrt{1-x^2}}$
$\displaystyle{\frac{1}{x}}$
$\displaystyle{\frac{\sqrt{x^2 + 16}}{4}}$
Write the given expression in terms of $x$ without any trigonometric functions:
$\sin(\arctan x)$
$\tan(\arcsin x)$
$\cot(\arcsin x)$
$\cos(\arcsin x)$
$\cos(\textrm{arcsec}\, x)$
$\csc(\textrm{arccot}\, \frac{x}{4})$
$\displaystyle{\frac{x}{\sqrt{x^2 + 1}}}$
$\displaystyle{\frac{x}{\sqrt{1-x^2}}}$
$\displaystyle{\frac{\sqrt{1-x^2}}{x}}$
$\displaystyle{\sqrt{1-x^2}}$
$\displaystyle{\frac{1}{x}}$
$\displaystyle{\frac{\sqrt{x^2 + 16}}{4}}$