Toán Lớp 11: Tìm tổng các nghiệm của PT 2cos (x – π/3) = 1 trên [ -π , π ]
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 11: Tìm tổng các nghiệm của PT 2cos (x – π/3) = 1 trên [ -π , π ]
Comments ( 1 )
2\cos \left( {x – \dfrac{\pi }{3}} \right) = 1\\
\Leftrightarrow \cos \left( {x – \dfrac{\pi }{3}} \right) = \dfrac{1}{2}\\
\Leftrightarrow \cos \left( {x – \dfrac{\pi }{3}} \right) = \cos \dfrac{\pi }{3}\\
\Leftrightarrow \left[ \begin{array}{l}
x – \dfrac{\pi }{3} = \dfrac{\pi }{3} + k2\pi \\
x – \dfrac{\pi }{3} = – \dfrac{\pi }{3} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{2\pi }}{3} + k2\pi \\
x = k2\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\\
TH1:\,\,\,x = \dfrac{{2\pi }}{3} + k2\pi \\
x \in \left[ { – \pi ;\pi } \right] \Rightarrow – \pi \le x \le \pi \\
\Leftrightarrow – \pi \le \dfrac{{2\pi }}{3} + k2\pi \le \pi \\
\Leftrightarrow – 1 \le \dfrac{2}{3} + 2k \le 1\\
\Leftrightarrow – \dfrac{5}{3} \le 2k \le \dfrac{1}{3}\\
\Leftrightarrow – \dfrac{5}{6} \le k \le \dfrac{1}{6}\\
k \in Z \Rightarrow k = 0 \Rightarrow x = \dfrac{{2\pi }}{3}\\
TH2:\,\,\,x = k2\pi \\
x \in \left[ { – \pi ;\pi } \right] \Rightarrow – \pi \le x \le \pi \\
\Rightarrow – \pi \le k2\pi \le \pi \\
\Rightarrow – 1 \le 2k \le 1\\
\Leftrightarrow – \dfrac{1}{2} \le k \le \dfrac{1}{2}\\
k \in Z \Rightarrow k = 0 \Rightarrow x = 0
\end{array}\)