Find the domain and range of `f(x)=sqrt((log)_3{"cos"(sinx)})`

Explanation

To find the domain and range of the function \( f(x) = \sqrt{\log_3(\cos(\sin x))} \), we will follow these steps:

### Step 1: Determine when the logarithm is defined
The logarithm \( \log_3(\cos(\sin x)) \) is defined when \( \cos(\sin x) > 0 \).

### Step 2: Analyze the cosine function
The cosine function, \( \cos(\theta) \), is positive when \( \theta \) is in the intervals \( (2n\pi - \frac{\pi}{2}, 2n\pi + \frac{\pi}{2}) \) for any integer \( n \). Thus, we need to find when \( \sin x \) falls within these intervals.

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