Sin (2x-10°)=1/2 với -120°

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Sin (2x-10°)=1/2 với -120°

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Khải Quang 4 years 2020-11-23T03:57:21+00:00 2 Answers 68 views 0

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  1. Philomena
    0
    2020-11-23T03:58:37+00:00
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    sin-2-10-1-2-voi-120-90

  2. Acacia
    0
    2020-11-23T03:58:52+00:00
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    `sin (2x – 10^0) = 1/2`

    `<=> sin (2x – 10^0) = sin 30^0`

    `<=>` \(\left[ \begin{array}{l}2x – 10^0 = 30^0 + k360^0\\2x – 10^0 = 150^0 + k360^0\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}2x = 40^0 + k360^0\\2x = 160^0 + k360^0\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}x = 20^0 + k180^0\\x = 80^0 + k180^0\end{array} \right.\) `(k ∈ ZZ)`

    Vậy 

    \(\left[ \begin{array}{l}-120^0 < 20^0 + k180^0 < 90^0\\-120^0 < 80^0 + k180^0 < 90^0\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}-140^0 < k180^0 < 70^0\\-200^0 < k180^0 < 10^0\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}-\dfrac{7}{9} < k < \dfrac{7}{18}\\-\dfrac{10}{9} < k < \dfrac{1}{18}\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}-0,8 < k < 0,39\\-1,11 < k < 0,056\end{array} \right.\) 

    `<=>` \(\left[ \begin{array}{l}k ∈ {-1; 0}\\k ∈ {0}\end{array} \right.\) 

    Vậy có 2 giá trị `k` là` {-1; 0}`

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )