To find the value of \( \sec(50^\circ) \), we first need to understand that \( \sec(x) \) is the reciprocal of the cosine function:
\[ \sec(x) = \frac{1}{\cos(x)} \]
Therefore, we need to calculate \( \cos(50^\circ) \) first.
Using a calculator,
\[ \cos(50^\circ) \approx 0.6428 \]
Now, we can find \( \sec(50^\circ) \):
\[ \sec(50^\circ) = \frac{1}{\cos(50^\circ)} \approx \frac{1}{0.6428} \approx 1.5557 \]
Rounding this to the nearest thousandth, we get:
\[ \sec(50^\circ) \approx 1.556 \]
Thus, the value of \( \sec(50^\circ) \) to the nearest thousandth is \( \boxed{1.556} \).
1 answer