Find the exact value of each expression, if it is defined. (If an answer is undefined, enter UNDEFINED.)(a)cos−1 22 (b)cos−1(1) (c)cos−1 − 22

1. Break Down the Problem

We need to evaluate three expressions involving the arccosine function ($\cos^{-1}$). We will analyze each expression:

• (a) $\cos^{-1}(22)$
• (b) $\cos^{-1}(1)$
• (c) $\cos^{-1}(-22)$

2. Relevant Concepts

The range of the arccosine function is defined for inputs in the interval $[-1, 1]$. Any value outside this range will be considered undefined.

3. Analysis and Detail

1. For (a) $\cos^{-1}(22)$:

   • Since $22$ is greater than $1$, this expression is undefined.

2. For (b) $\cos^{-1}(1)$:

   • $\cos(0) = 1$ implies $\cos^{-1}(1) = 0$.

3. For (c) $\cos^{-1}(-22)$:

   • Since $-22$ is less than $-1$, this expression is also undefined.

4. Verify and Summarize

• The expressions for (a) and (c) have values that fall outside the arccos function's defined range. Only (b) yields a valid result.

Final Answer

(a) UNDEFINED
(b) 0
(c) UNDEFINED