The principal value of ${\sin ^{ - 1}}\left( { - \frac{1}{2}} \right)$ is

The cumulative number of ill patients $N( t )$ during an epidemic in a country is given by the following equation $N(t)=\frac{N_0 \exp (t / \tau)}{1+N_0(\exp (t / \tau)-1) / N_s}$ where $N _0$ is the initial population of ill patients, $\tau$ a positive constant and $N _5\left( > > N _0\right)$ is a large number. Then, which of the following statements is true ?