Decide whether the statement is possible or impossible for an angle θ.
-$$\sec \theta = - 0.75$$
A) Impossible
B) Possible

Question

Quizplus · Accepted Answer

The secant function, $\sec \theta$, is the reciprocal of the cosine function, $\cos \theta$. Since the range of $\cos \theta$ is $[-1, 1]$, the range of $\sec \theta$ is $(-\infty, -1] \cup [1, \infty)$. Therefore, $\sec \theta = -0.75$ is impossible because $-0.75$ is not within the range of the secant function.

Decide Whether the Statement Is Possible or Impossible for an Angle