https://file.aiquickdraw.com/mathbot/file/17262633868674y48gpgr.jpg

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.

Find the exact value, in radians, of the expression sin^(-1)(√2/2). Use a graph of y = sin^(-1)(x).

Learn how to find the exact value of the inverse sine function sin^(-1)(√2/2) in radians. Understand the relation between the angle π/4 and the trigonometric identity sin(π/4) = √2/2. Suitable for high school students studying trigonometry.

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