## Trigonometry 7th Edition

$\cos{\theta} = \dfrac{x}{r}$. Since $r \ge x$, then the value of $\dfrac{x}{r}$, which is also the value of $\cos{\theta}$, will always be less than or equal to $1$.
Definition I states that $\cos{\theta}= \dfrac{x}{r}$. Figure 1 shows that $r$ is the hypotenuse (longest side) of the right triangle, while $x$ and $y$ are the legs. Since $r\ge x$, then $\frac{x}{r}$ will be less than or equal to $1$ Thus,for any angle in standard position, $\cos{\theta} \le 1$.