Pregunta
\( 2 \sin x-1=0 \), find \( x \) if \( 0^{\circ} \leqslant x \leqslant 360^{\circ} \)
Ask by Christensen Ellis. in Nigeria
Mar 20,2025
Solución de inteligencia artificial de Upstudy
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The solutions are \( x = 30^\circ \) and \( x = 150^\circ \).
Solución
1. Start with the equation:
\[
2 \sin x - 1 = 0
\]
2. Add 1 to both sides:
\[
2 \sin x = 1
\]
3. Divide both sides by 2:
\[
\sin x = \frac{1}{2}
\]
4. Find all angles \( x \) in the interval \( 0^\circ \leqslant x \leqslant 360^\circ \) where \( \sin x = \frac{1}{2} \).
We know that:
\[
\sin 30^\circ = \frac{1}{2} \quad \text{and} \quad \sin 150^\circ = \frac{1}{2}
\]
5. Therefore, the solutions are:
\[
x = 30^\circ \quad \text{and} \quad x = 150^\circ
\]
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Simplifique esta solución Mind Expander
To solve the equation \( 2 \sin x - 1 = 0 \), we first isolate \( \sin x \) by adding 1 to both sides and then dividing by 2: \[ \sin x = \frac{1}{2} \] Now, we find the angles within the interval \( 0^{\circ} \leqslant x \leqslant 360^{\circ} \) where the sine value equals \( \frac{1}{2} \). The sine function equals \( \frac{1}{2} \) at the angles: \[ x = 30^{\circ} \quad \text{and} \quad x = 150^{\circ} \] Thus, the solutions are: \[ x = 30^{\circ} \quad \text{and} \quad x = 150^{\circ} \] In summary, \( x \) can be \( 30^{\circ} \) or \( 150^{\circ} \).
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