A signal is s(t) = sin⁻¹(sin 2t) radians, where t is the time in seconds and 2t is in radians…

Step 1. At $t = 1.2\ \text{s}$. $2t = 2.4$, which is between $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$. So $s = \pi - 2.4 = 0.7416$ rad.

Step 2. At $t = 2.3\ \text{s}$. $2t = 4.6$, which is still between $1.5708$ and $4.7124$. So $s = \pi - 4.6 = -1.4584$ rad.

Step 3. The period. The signal repeats when $2t$ grows by $2\pi$, that is when $t$ grows by $\pi$. The period is $\pi\ \text{s} = 3.1416\ \text{s}$.