## Trigonometry 7th Edition

With $\csc{\theta} = \dfrac{r}{y}$ and $r \ge |y|$, then $|\csc{\theta}|\ge1$ for any angle in standard position since the value of $|\frac{r}{y}|$ will never be less than $1$. Refer to the step-by-step part for the explanation.
Definition I states that $\csc{\theta}= \dfrac{r}{y}, y\ne0$. 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 or equal to $|y|$, then $|\frac{r}{y}|$ will be never smaller than $1$ Thus,for any angle in standard position, $|\csc{\theta}|$ will always be greater than or equal to $1$.