The expression you provided is $\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)$.

This expression represents the inverse cosine (or arccosine) of $\frac{\sqrt{2}}{2}$.

Solution:

To find the value of $\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)$, we need to determine the angle whose cosine is $\frac{\sqrt{2}}{2}$.

We know that: $\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

Therefore: $\cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4} \text{ radians}$ Or equivalently: $\cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = 45^\circ$

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Related Questions:

1. What is the value of $\cos^{-1}(0)$?
2. How do you solve $\cos^{-1}\left(\frac{1}{2}\right)$?
3. What is the domain of the inverse cosine function?
4. How can you express $\cos^{-1}$ in terms of trigonometric identities?
5. What is the difference between $\cos^{-1}$ and $\sec^{-1}$?

Tip:

The inverse trigonometric functions return the angle that corresponds to a given trigonometric ratio, typically within a specific range.