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: 36


There is no angle $\theta$ whose secant value is $\frac{1}{2}$ because the value of $\sec{\theta}$ will never be less than $1$.

Work Step by Step

Definition I states that $\sec{\theta}= \dfrac{r}{x}, x\ne0$. Figure 1 shows that $r$ is the hypotenuse (longest side) of the right triangle, while $x$ and $y$ are the legs. Since $r$ is longer than $x$, $\dfrac{r}{x}$ will never be smaller than $1$. Thus, there will be no angle $\theta$ whose secant value is $\frac{1}{2}$.
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