# Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 35

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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