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The given expression evaluates to approximately \( 3.927 \) (radians).

The steps to evaluate this are as follows:

1. \( \sin^{-1}(\sin(3\pi/4)) \) results in \( \pi/4 \), since the range of \( \sin^{-1} \) is \( [-\pi/2, \pi/2] \).
2. \( \cos^{-1}(\cos(3\pi/4)) \) is \( 3\pi/4 \), as the range of \( \cos^{-1} \) is \( [0, \pi] \).
3. \( \tan^{-1}(1) \) results in \( \pi/4 \), since the tangent of \( 1 \) is \( \pi/4 \).

Adding these together gives:

\[
\frac{\pi}{4} + \frac{3\pi}{4} + \frac{\pi}{4} = \frac{5\pi}{4} \approx 3.927 \text{ radians}.
\]

Let me know if you'd like any further details or have questions!

Here are five related questions:

1. What is the range of the inverse sine function?
2. How do you derive the value of \( \tan^{-1}(1) \)?
3. What is the difference between radians and degrees in angular measurements?
4. Can you apply similar evaluations to other inverse trigonometric functions?
5. How do inverse trigonometric functions relate to right triangles?

**Tip:** Inverse trigonometric functions return angles, so it's important to be aware of their ranges when solving problems.

sin^(-1)(sin(3π/4)) + cos^(-1)(cos(3π/4)) + tan^(-1)(1/1)

Explore the evaluation of the expression sin^(-1)(sin(3π/4)) + cos^(-1)(cos(3π/4)) + tan^(-1)(1), involving inverse trigonometric functions. Learn key concepts and formulas including inverse sine, cosine, and tangent properties. Suitable for students in Grades 10-12.

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