Solve the equation sin 5/2ø= 1/2 for 0⁰<ø< 180⁰

Step 1: The general solution for $\sin \phi = \frac{1}{2}$ is
$\phi = 30^\circ + 360^\circ n \quad or \quad \phi = 150^\circ + 360^\circ n,$
where $n$ is any integer.

Step 2: Substitute $\phi = \frac{5}{2} \theta$.
$\frac{5}{2} \theta = 30^\circ + 360^\circ n \quad or \quad \frac{5}{2} \theta = 150^\circ + 360^\circ n.$

Step 3: Solve for $\theta$.
First equation:
$\theta = \frac{2}{5} (30^\circ + 360^\circ n) = 12^\circ + 144^\circ n.$
Second equation:
$\theta = \frac{2}{5} (150^\circ + 360^\circ n) = 60^\circ + 144^\circ n.$

Step 4: Apply $0^\circ < \theta < 180^\circ$.

For $\theta = 12^\circ + 144^\circ n$:

• $n=0$: $\theta = 12^\circ$
• $n=1$: $\theta = 156^\circ$
• $n=2$: $\theta = 300^\circ > 180^\circ$
• $n=-1$: $\theta = -132^\circ < 0^\circ$

For $\theta = 60^\circ + 144^\circ n$:

• $n=0$: $\theta = 60^\circ$
• $n=1$: $\theta = 204^\circ > 180^\circ$
• $n=-1$: $\theta = -84^\circ < 0^\circ$

Solutions: $\theta = 12^\circ, 60^\circ, 156^\circ$
$\boxed{12^\circ, 60^\circ, 156^\circ}$