Question:
If
\[
2 \sin 2\theta = \sqrt{3},
\]
then \(\theta =\)?
If
\[
2 \sin 2\theta = \sqrt{3},
\]
then \(\theta =\)?
Show Hint
Divide both sides by constants to isolate \(\sin 2\theta\), then use inverse sine and consider the principal domain.
Updated On: Jul 18, 2026
- \(15^\circ\)
- \(27^\circ\)
- \(30^\circ\)
- \(40^\circ\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Write equation.
\[ 2 \sin 2\theta = \sqrt{3} \Rightarrow \sin 2\theta = \frac{\sqrt{3}}{2} \]
Step 2: Find possible angles for \(2\theta\).
\[ 2\theta = 60^\circ, 120^\circ \quad (\text{principal solutions}) \]
Step 3: Solve for \(\theta\).
\[ \theta = 30^\circ, 60^\circ \]
Step 4: Consider domain or context.
Assuming \(\theta \in [0, 90^\circ]\), the smallest positive solution is \(\theta = 30^\circ\).
Step 5: Final conclusion.
\[ \boxed{30^\circ} \]
\[ 2 \sin 2\theta = \sqrt{3} \Rightarrow \sin 2\theta = \frac{\sqrt{3}}{2} \]
Step 2: Find possible angles for \(2\theta\).
\[ 2\theta = 60^\circ, 120^\circ \quad (\text{principal solutions}) \]
Step 3: Solve for \(\theta\).
\[ \theta = 30^\circ, 60^\circ \]
Step 4: Consider domain or context.
Assuming \(\theta \in [0, 90^\circ]\), the smallest positive solution is \(\theta = 30^\circ\).
Step 5: Final conclusion.
\[ \boxed{30^\circ} \]
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