Evaluate each expression.
$\(\sec\[\left\)(\(\frac{\pi}{3}\]\right\))$

• A. $\(\frac\)12$
• B. $2$
• C. $\(\frac{\sqrt3}{2}\)$
• D. $\(\frac{2\sqrt3}{2}\)$

Answer: (B)

Verified step by step guidance

1. Understand that secant, \( \sec(\theta) \), is the reciprocal of cosine, \( \cos(\theta) \). Therefore, \( \sec\left(\frac{\pi}{3}\right) = \frac{1}{\cos\left(\frac{\pi}{3}\right)} \).
2. Recall the value of \( \cos\left(\frac{\pi}{3}\right) \). From the unit circle or trigonometric tables, \( \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} \).
3. Substitute the value of \( \cos\left(\frac{\pi}{3}\right) \) into the secant expression: \( \sec\left(\frac{\pi}{3}\right) = \frac{1}{\frac{1}{2}} \).
4. Simplify the expression \( \frac{1}{\frac{1}{2}} \) to find the value of \( \sec\left(\frac{\pi}{3}\right) \).
5. Conclude that the simplified value of \( \sec\left(\frac{\pi}{3}\right) \) is 2.