Cho π/2 <α<πxét dấu hàm lượng giác sau a) sin (α-3π/2) b) cot (π/2-α) c) cos (α-3π/2) d) tan(π/2+α) e) cot(5π/2-α) d) sin(α+3π/2)
Cho π/2 <α<πxét dấu hàm lượng giác sau a) sin (α-3π/2) b) cot (π/2-α) c) cos (α-3π/2) d) tan(π/2+α) e) cot(5π/2-α) d) sin(α+3π/2)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow – \pi < \alpha – \frac{{3\pi }}{2} < – \frac{\pi }{2} \Rightarrow \sin \left( {\alpha – \frac{{3\pi }}{2}} \right) < 0\\
b,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow – \frac{\pi }{2} < \frac{\pi }{2} – \alpha < 0 \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{\pi }{2} – \alpha } \right) < 0\\
\cos \left( {\frac{\pi }{2} – \alpha } \right) > 0
\end{array} \right. \Rightarrow \cot \left( {\frac{\pi }{2} – \alpha } \right) < 0\\
c,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow – \pi < \alpha – \frac{{3\pi }}{2} < – \frac{\pi }{2} \Rightarrow \cos \left( {\alpha – \frac{{3\pi }}{2}} \right) < 0\\
d,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow \pi < \frac{\pi }{2} + \alpha < \frac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{\pi }{2} + \alpha } \right) < 0\\
\cos \left( {\frac{\pi }{2} + \alpha } \right) < 0
\end{array} \right. \Rightarrow \tan \left( {\frac{\pi }{2} + \alpha } \right) > 0\\
e,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow \frac{{3\pi }}{2} < \frac{{5\pi }}{2} – \alpha < 2\pi \Rightarrow \left\{ \begin{array}{l}
\sin \left( {\frac{{5\pi }}{2} – \alpha } \right) < 0\\
\cos \left( {\frac{{5\pi }}{2} – \alpha } \right) > 0
\end{array} \right. \Rightarrow \cot \left( {\frac{{5\pi }}{2} – \alpha } \right) < 0\\
f,\\
\frac{\pi }{2} < \alpha < \pi \Rightarrow 2\pi < \alpha + \frac{{3\pi }}{2} < \frac{{5\pi }}{2} \Rightarrow \sin \left( {\alpha + \frac{{3\pi }}{2}} \right) > 0
\end{array}\)
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