## Trigonometry 7th Edition

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