Question

evaluate the following expression. \\(\cos^{-1}(1)\\) answer choices: \\(2\pi\\), \\(-\pi\\), undefined, \\(0\\)

Explanation:

Step1: Recall the range of arccosine function

The arccosine function, \( \cos^{-1}(x) \), has a range of \( [0, \pi] \). This means the output of \( \cos^{-1}(x) \) must be between \( 0 \) and \( \pi \) (inclusive).

Step2: Evaluate \( \cos^{-1}(1) \)

We know from the unit circle and the definition of cosine that \( \cos(0) = 1 \). Since \( 0 \) is within the range \( [0, \pi] \) of the arccosine function, \( \cos^{-1}(1) = 0 \).

Answer:

\( 0 \) (the option with the value \( 0 \))