## Sin (2x-10°)=1/2 với -120°

Question

Sin (2x-10°)=1/2 với -120°

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

1. Bạn xem hình

2. 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}