[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Evaluate the following

• [math]\arcsin 1[/math]
• [math]\arcsin \frac12[/math]
• [math]\arccos \frac12[/math]
• [math]\arcsin \left(- \frac{\sqrt3}2\right)[/math]
• [math]\arctan \sqrt3[/math]
• [math]\arccot \sqrt{3}[/math]
• [math]\arcsec \left( \frac2{\sqrt3}\right)[/math]
• [math]\arccsc 2[/math]
• [math]\arcsin (\sin a)[/math]
• [math]\arctan \left( \tan \frac{\pi}7 \right)[/math]
• [math]\arctan \left( \cot \frac{\pi}7 \right)[/math]
• [math]\arcsin (\cos a)[/math]
• [math]\tan [\arctan (-1)][/math]
• [math]\arcsin (2 \sin x \cos x)[/math]
• [math]\arcsin \left( \sin \frac{3\pi}4 \right)[/math]
• [math]\arctan \left( \cot \frac{\pi}6 \right)[/math].