Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 42


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,
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