Evaluate the following expression:
`sin("cos"^(-1)3/5)`

Explanation

To evaluate the expression \( \sin(\cos^{-1}(\frac{3}{5})) \), we can follow these steps:

### Step 1: Let \( \theta = \cos^{-1}(\frac{3}{5}) \)
This means that \( \cos(\theta) = \frac{3}{5} \).

### Step 2: Use the Pythagorean identity to find \( \sin(\theta) \)
We know that:
\[ \sin^2(\theta) + \cos^2(\theta) = 1 \]
Substituting \( \cos(\theta) = \frac{3}{5} \):
\[ \sin^2(\theta) + \left(\frac{3}{5}\right)^2 = 1 \]
\[ \sin^2(\theta) + \frac{9}{25} = 1 \]

### Step 3: Solve for \( \sin^2(\theta) \)
Rearranging the equation gives:
\[ \sin^2(\theta) = 1 - \frac{9}{25} \]
To combine the terms, convert 1 to a fraction:
\[ 1 = \frac{25}{25} \]
Thus,
\[ \sin^2(\theta) = \frac{25}{25} - \frac{9}{25} = \frac{16}{25} \]

### Step 4: Take the square root to find \( \sin(\theta) \)
\[ \sin(\theta) = \sqrt{\frac{16}{25}} = \frac{4}{5} \]
Since \( \theta = \cos^{-1}(\frac{3}{5}) \) is in the range \( [0, \pi] \), \( \sin(\theta) \) is positive.

### Step 5: Substitute back to find the final answer
Thus, we have:
\[ \sin(\cos^{-1}(\frac{3}{5})) = \frac{4}{5} \]

### Final Answer
The value of \( \sin(\cos^{-1}(\frac{3}{5})) \) is \( \frac{4}{5} \).

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