Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
20,\\
x = \frac{{3\pi }}{4} \Rightarrow \frac{\pi }{2} < x < \pi \Rightarrow \left\{ \begin{array}{l}
\sin x > 0\\
\cos x < 0
\end{array} \right.\\
\tan x = \frac{{\sin x}}{{\cos x}} < 0,\,\,\,\,\,\,\,\cot x = \frac{{\cos x}}{{\sin x}} < 0\\
21,\\
\sin \frac{{49\pi }}{6} = \sin \left( {8\pi + \frac{\pi }{6}} \right) = \sin \frac{\pi }{6} = \frac{1}{2}\\
23,\\
x \in \left( {\frac{\pi }{2};\pi } \right) \Rightarrow \frac{\pi }{2} < \frac{{3\pi }}{2} - x < \pi \Rightarrow \sin \left( {\frac{{3\pi }}{2} - x} \right) > 0\\
24,\\
A = \cos \frac{\pi }{9} + \cos \frac{{5\pi }}{9} + \cos \frac{{7\pi }}{9}\\
= \cos 20^\circ + \cos 100^\circ + \cos 140^\circ \\
= \cos 20^\circ - \cos \left( {180^\circ - 100^\circ } \right) - \cos \left( {180^\circ - 140^\circ } \right)\\
= \cos 20^\circ - \cos 80^\circ - \cos 40^\circ \\
= \cos 20^\circ - \left( {\cos 80^\circ + \cos 40^\circ } \right)\\
= \cos 20^\circ - 2.\cos 60^\circ .\cos 20^\circ \\
= \cos 20^\circ \left( {1 - 2\cos 60^\circ } \right)\\
= \cos 20^\circ .\left( {1 - 2.\frac{1}{2}} \right) = 0\\
25,\\
s = \frac{{\frac{\pi }{{15}}}}{{2\pi }}.2.R.\pi = 4,19
\end{array}\)
