Trigonometry 7th Edition

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

Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set - Page 62: 21


With $\cos{\theta} = \dfrac{\text{length of side adjacent to A}}{\text{length of hypotenuse}}$, and since the hypotenuse is longer than the two other sides of the triangle, then the value of $\cos{\theta}$ will always never be greater than 1. Thus, it is impossible for $\cos{\theta} = 3$.

Work Step by Step

Definition II states that in a right triangle with acute angle A, $\cos{A}=\dfrac{\text{length of side adjacent to A}}{\text{length of hypotenuse}}=\dfrac{b}{c},$ where $c$ = length of hypotenuse $b$ = length of side adjacent to angle A. Since $c \gt b$, then the value of $\dfrac{b}{c}$ will always be less than $1$. Thus, there will be no angle whose cosine value is greater than $1$.
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