If `K=sin(pi/(18))sin((5pi)/(18))sin((7pi)/(18)),` then the numerical value of `K` is_____

Explanation

To find the numerical value of \( K = \sin\left(\frac{\pi}{18}\right) \sin\left(\frac{5\pi}{18}\right) \sin\left(\frac{7\pi}{18}\right) \), we can follow these steps:

### Step 1: Rewrite the Sine Functions
We can use the identity \( \sin\left(\frac{5\pi}{18}\right) = \sin\left(\frac{\pi}{2} - \frac{4\pi}{18}\right) = \cos\left(\frac{4\pi}{18}\right) \) and \( \sin\left(\frac{7\pi}{18}\right) = \sin\left(\frac{\pi}{2} - \frac{2\pi}{18}\right) = \cos\left(\frac{2\pi}{18}\right) \).

So, we rewrite \( K \):
\[
K = \sin\left(\frac{\pi}{18}\right) \cos\left(\frac{4\pi}{18}\right) \cos\left(\frac{2\pi}{18}\right)
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