Cho $0 < \alpha < \frac{\pi}{2}.$ Xét dấu của các biểu thức sau: a) $A = cos(\alpha + \pi)$ b) $B = tan(\alpha - \pi)$ c) $C = sin(\alpha + \frac{2\pi}{5})$ d) $D = sin(\alpha - \frac{3\pi}{8})$
Cho $0 < \alpha < \frac{\pi}{2}.$ Xét dấu của các biểu thức sau: a) $A = cos(\alpha + \pi)$ b) $B = tan(\alpha - \pi)$ c) $C = sin(\alpha + \frac{2\pi}{5})$ d) $D = sin(\alpha - \frac{3\pi}{8})$
Đáp án:
$\begin{array}{l}
0 < \alpha < \frac{\pi }{2}\\
a)\pi < \alpha + \pi < \frac{{3\pi }}{2}\\
\Rightarrow \cos \left( {\alpha + \pi } \right) < 0\\
\Rightarrow A < 0\\
b)\\
– \pi < \alpha – \pi < – \frac{\pi }{2}\\
\Rightarrow \left\{ \begin{array}{l}
\sin \left( {\alpha – \pi } \right) < 0\\
\cos \left( {\alpha – \pi } \right) < 0
\end{array} \right.\\
\Rightarrow \tan \left( {\alpha – \pi } \right) > 0\\
\Rightarrow B > 0\\
c)\frac{{2\pi }}{5} < \alpha + \frac{{2\pi }}{5} < \frac{{9\pi }}{{10}}\\
\Rightarrow \sin \left( {\alpha + \frac{{2\pi }}{5}} \right) > 0\\
\Rightarrow C > 0\\
d) – \frac{{3\pi }}{8} < \alpha – \frac{{3\pi }}{8} < \frac{\pi }{8}\\
\Rightarrow \left\{ \begin{array}{l}
\sin \left( {\alpha – \frac{{3\pi }}{8}} \right) < 0\,khi: – \frac{{3\pi }}{8} < x < 0\\
\sin \left( {\alpha – \frac{{3\pi }}{8}} \right) \ge 0\,khi:0 \le x \le \frac{\pi }{8}
\end{array} \right.
\end{array}$