Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 41

From $0^o$ to $90^o$, the angle $\theta$ increases, the value of $\tan{\theta}$ tends toward positive infinity.

Work Step by Step

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.

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