The expression in the image is asking to find the exact value of the inverse sine (also known as arcsin) of $\frac{\sqrt{2}}{2}$, in radians. It also suggests using the graph of $y = \sin^{-1}(x)$ to help.

Let's break it down:

1. We need to find: $\sin^{-1}\left(\frac{\sqrt{2}}{2}\right)$

2. From trigonometric values, we know that: $\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

3. Therefore: $\sin^{-1}\left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4}$

This means the exact value of $\sin^{-1}\left(\frac{\sqrt{2}}{2}\right)$ is $\frac{\pi}{4}$ radians.

Would you like more details on how the inverse sine function works or why this specific angle corresponds to $\frac{\pi}{4}$? Here are 5 related questions to explore further:

1. What is the domain and range of the arcsin function?
2. How can you graph the $y = \sin^{-1}(x)$ function manually?
3. What are the other common exact values of inverse sine?
4. How can you apply the inverse sine in real-world problems?
5. What is the significance of radian measure in trigonometry?

Tip: When working with inverse trigonometric functions, it's important to remember their specific ranges. For $\sin^{-1}(x)$, the range is from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$, so the function always returns an angle in this interval.