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Evaluate each of the following: sin...

Evaluate each of the following:

`sin^(-1)(sin3)`

(ii) `sin^(-1)(sin4)`

Text Solution

AI Generated Solution

To evaluate the expressions \( \sin^{-1}(\sin 3) \) and \( \sin^{-1}(\sin 4) \), we need to understand the properties of the inverse sine function and the sine function. ### Step-by-Step Solution: 1. **Understanding the Range of \( \sin^{-1}(x) \)**: The function \( \sin^{-1}(x) \) (or arcsin) has a range of \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \). This means that for any angle \( x \) outside this range, we need to find a corresponding angle within this range that has the same sine value. 2. **Evaluating \( \sin^{-1}(\sin 3) \)**: ...
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