Equations - Trigonometric Equation Sin

Trigonometric Equations: Sine

\[ \sin x = m \]

If \(|m| \leq 1\), the solutions are:

\[ x_1 = \alpha + 2k_1 \pi, \quad k_1 \in \mathbb{Z} \]

\[ x_2 = (\pi - \alpha) + 2k_2 \pi, \quad k_2 \in \mathbb{Z} \]

where \(\alpha = \arcsin m\), and \(-\frac{\pi}{2} \leq \alpha \leq \frac{\pi}{2}\).

If \(|m| > 1\), there is no real solution.

Trigonometric Equations Sin
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