To find the value of \(\sec(39^\circ)\), we first need to calculate the cosine of \(39^\circ\) and then take its reciprocal:
\[ \sec(39^\circ) = \frac{1}{\cos(39^\circ)} \]
Using a calculator:
\[ \cos(39^\circ) \approx 0.7771 \]
Therefore:
\[ \sec(39^\circ) \approx \frac{1}{0.7771} \approx 1.285 \]
When rounded to the nearest thousandths, the value is:
\[ \sec(39^\circ) \approx 1.285 \]
So, the final answer to the nearest thousandths is approximately 1.285.
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