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: 35

Answer

There is no angle $\theta$ whose sine value is $2$ because the maximum value of $\sin{\theta}$ is 1.

Work Step by Step

Definition I states that $\sin{\theta}= \dfrac{y}{r}$. 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 $y$, then $\dfrac{y}{r}$ will never be greater than $1$. Thus, there will be no angle $\theta$ whose sine value is $2$.
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