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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: giúp em với : sin ( 2x – pi / 6 ) = 1 / 2

Tháng Hai 2, 2023 Toán học 2 Comments 0 views

Toán Lớp 11: giúp em với : sin ( 2x – pi / 6 ) = 1 / 2

Comments ( 2 )

  1. tonhu12
    tonhu12
    2 Tháng Hai, 2023 at 7:32 sáng
    Reply
    ~rai~
    \(\sin\left(2x-\dfrac{\pi}{6}\right)=\dfrac{1}{2}\\\Leftrightarrow \left[\begin{array}{I}2x-\dfrac{\pi}{6}=\dfrac{\pi}{6}+k2\pi\\2x-\dfrac{\pi}{6}=\pi-\dfrac{\pi}{6}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}2x=\dfrac{\pi}{6}+\dfrac{\pi}{6}+k2\pi\\2x=\pi-\dfrac{\pi}{6}+\dfrac{\pi}{6}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}2x=\dfrac{\pi}{3}+k2\pi\\2x=\pi+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{\pi}{2}+k\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy phương trình có các họ nghiệm là:}\\x=\dfrac{\pi}{6}+k\pi;x=\dfrac{\pi}{2}+k\pi.(k\in\mathbb{Z})\)
     

  2. tuyetanhthu
    tuyetanhthu
    2 Tháng Hai, 2023 at 7:32 sáng
    Reply
    Ta có:
    \qquad sin(2x-π/6)=1/2
    <=> sin(2x-π/6)=sin\ π/6
    <=>$\left[\begin{array}{l}2x-\dfrac{π}{6}=\dfrac{π}{6}+k2π\\2x-\dfrac{π}{6}=π-\dfrac{π}{6}+k2π\end{array}\right.\ (k\in Z)$
    <=>$\left[\begin{array}{l}2x=\dfrac{π}{3}+k2π\\2x=π+k2π\end{array}\right.\ (k\in Z)$
    <=>$\left[\begin{array}{l}x=\dfrac{π}{6}+kπ\\x=\dfrac{π}{2}+kπ\end{array}\right.\ (k\in Z)$

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222-9+11+12:2*14+14 = ? ( )

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