Find the exact value of the real number y.       Y= sin^-1 (1)

To find the exact value of \( y = \sin^{-1}(1) \), we need to determine the angle \( y \) for which \( \sin(y) = 1 \).

The sine of an angle is equal to 1 at \( y = \frac{\pi}{2} \) radians (or 90°) within the principal range of the inverse sine function, which is \( -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \).

Thus, the exact value of \( y \) is:

\[
y = \frac{\pi}{2}
\]

Would you like more details on inverse trigonometric functions or their ranges?

Here are 5 related questions you might explore:
1. What is the value of \( \sin^{-1}(0) \)?
2. What is the range of the inverse sine function?
3. How would you solve \( y = \sin^{-1}(-1) \)?
4. Can you find the derivative of \( \sin^{-1}(x) \)?
5. What are the values of \( \sin^{-1}(\frac{1}{2}) \)?

**Tip:** Inverse trigonometric functions can help solve equations involving angles and their trigonometric values. Always remember the principal range when dealing with inverse functions.

Find the exact value of the real number y. Y = sin^-1 (1)

Discover the exact value of y for the equation y = sin^-1(1). Learn how to solve this trigonometric problem by using the inverse sine function and its principal range. This problem is perfect for students in Grades 9-11 and covers key concepts in trigonometry and inverse functions.

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