Answer
In the interval $0^o$ to $90^o$, the value of $\sec{\theta}$ tends toward positive infinity.
Work Step by Step
The secant function is increasing in the interval $(0, 90)$ and is undefined when $\theta=90^o$. The graph of secant is asymptotic to the line $\theta=90^o$.
Thus, as $\theta$ approaches $90^o$, the value of secant gets bigger and bigger without bound.
Therefore, as the angle $\theta$ increases from $0^o$ to $90^o$, the value of secant approaches positive infinity,
