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Solve the equation sin(5/2) θ = 1/2 for 0° ≤ θ ≤ 180°.

March 16, 2026Mathematics

ScanSolve AI Answer

Answer

\theta = 60^\circ, 120^\circ

5 steps

Given equation
$\sin \theta = \frac{\sqrt{3}}{2}$
Sine is positive in Quadrant I and Quadrant II.
Reference angle $\alpha$ satisfies $\sin \alpha = \frac{\sqrt{3}}{2}$ .
Standard value: $\alpha = 60^\circ$ .
Quadrant I solution
$\theta = \alpha = 60^\circ$
Quadrant II solution
Principal value is $180^\circ$ .
$\theta = 180^\circ - \alpha = 180^\circ - 60^\circ = 120^\circ$
Verify solutions in $[0^\circ, 360^\circ]$
$\sin 60^\circ = \frac{\sqrt{3}}{2}$ and $\sin 120^\circ = \frac{\sqrt{3}}{2}$ .
No other solutions.

Final answers: $\theta = 60^\circ, 120^\circ$

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