Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 264: 48

$\theta$ does not exist

RECALL: The range of the cosine function $y=\cos{x}$ is $[-1, 1]$. $\theta=\cos^{-1}{(-2)}$ means $\cos{\theta}=-2$ Since the range of the cosine function is only from -1 to 1, then no angle would have a cosine value of $-2$. Thus, there is no angle $\theta$ such that $\cos{\theta} = -2$.