using the appropriate table, find the exact value of sec pi/3

To find the exact value of \( \sec \left( \frac{\pi}{3} \right) \), we can use the trigonometric identity for secant:

\[
\sec \theta = \frac{1}{\cos \theta}
\]

For \( \theta = \frac{\pi}{3} \), we need to know the value of \( \cos \left( \frac{\pi}{3} \right) \). From the standard trigonometric table, we know that:

\[
\cos \left( \frac{\pi}{3} \right) = \frac{1}{2}
\]

Now, apply the secant formula:

\[
\sec \left( \frac{\pi}{3} \right) = \frac{1}{\cos \left( \frac{\pi}{3} \right)} = \frac{1}{\frac{1}{2}} = 2
\]

So, the exact value of \( \sec \left( \frac{\pi}{3} \right) \) is \( 2 \).

Would you like more details or have any questions about this? Here are 5 related questions to explore:

1. What is the exact value of \( \sec \left( \frac{\pi}{6} \right) \)?
2. How do you calculate \( \sec \theta \) for an angle not on the unit circle?
3. Can you express \( \sec \theta \) in terms of \( \sin \theta \)?
4. What is the relationship between secant and cosine functions?
5. How would you solve \( \sec \theta = 2 \) for \( \theta \)?

**Tip**: For angles on the unit circle, always recall their basic sine and cosine values to quickly find secant, cosecant, tangent, and cotangent.

Find the exact value of sec(π/3) using the trigonometric table. This step-by-step solution covers key trigonometric concepts like secant, cosine, and the unit circle. Perfect for high school students in Grades 9-12 looking to master trigonometry.

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