Tính E = sin π/5 + sin 2π/5 + … + Sin 9π/5 29/10/2021 Bởi Peyton Tính E = sin π/5 + sin 2π/5 + … + Sin 9π/5
$E= sin(\frac{\pi}{5})+sin(\frac{2\pi}{5})+ sin(\frac{3\pi}{5})+ sin(\frac{4\pi}{5})+ sin\pi+ sin(\pi+ \frac{\pi}{5})+ sin(\pi+\frac{2\pi}{5})+ sin(\pi+\frac{3\pi}{5})+ sin(\pi+\frac{9\pi}{5})$ Do $sin(\pi+\alpha)= -sin\alpha$ $\Rightarrow E= sin\pi= 0$ Bình luận
Đáp án: $E=0$ Giải thích các bước giải: $E=\sin \dfrac{\pi}{5}+\sin \dfrac{2\pi}{5}+…+\sin \dfrac{9\pi}{5}\\=\left ( \sin\dfrac{\pi}{5}+\sin\dfrac{9\pi}{5} \right )+\left ( \sin\dfrac{2\pi}{5}+\sin\dfrac{8\pi}{5} \right )+…+\left ( \sin\dfrac{4\pi}{5}+\sin\dfrac{6\pi}{5} \right )+\sin\dfrac{5\pi}{5}\\=0+0+…+0+\sin \pi\\=0$ Bình luận
$E= sin(\frac{\pi}{5})+sin(\frac{2\pi}{5})+ sin(\frac{3\pi}{5})+ sin(\frac{4\pi}{5})+ sin\pi+ sin(\pi+ \frac{\pi}{5})+ sin(\pi+\frac{2\pi}{5})+ sin(\pi+\frac{3\pi}{5})+ sin(\pi+\frac{9\pi}{5})$
Do $sin(\pi+\alpha)= -sin\alpha$
$\Rightarrow E= sin\pi= 0$
Đáp án:
$E=0$
Giải thích các bước giải:
$E=\sin \dfrac{\pi}{5}+\sin \dfrac{2\pi}{5}+…+\sin \dfrac{9\pi}{5}\\
=\left ( \sin\dfrac{\pi}{5}+\sin\dfrac{9\pi}{5} \right )+\left ( \sin\dfrac{2\pi}{5}+\sin\dfrac{8\pi}{5} \right )+…+\left ( \sin\dfrac{4\pi}{5}+\sin\dfrac{6\pi}{5} \right )+\sin\dfrac{5\pi}{5}\\
=0+0+…+0+\sin \pi\\
=0$