Trigonometry 7th Edition

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