To find the exact value of \(\sec 300^\circ\), we can follow these steps:

1. **Recall the definition of secant**:
   \[
   \sec \theta = \frac{1}{\cos \theta}
   \]

2. **Determine \(\cos 300^\circ\)**:
   \(300^\circ\) is in the fourth quadrant. In the fourth quadrant, the cosine of an angle is positive. The reference angle for \(300^\circ\) is:
   \[
   360^\circ - 300^\circ = 60^\circ
   \]
   Therefore, \(\cos 300^\circ\) is the same as \(\cos 60^\circ\), but with a positive value since \(\cos\) is positive in the fourth quadrant:
   \[
   \cos 300^\circ = \cos 60^\circ = \frac{1}{2}
   \]

3. **Calculate \(\sec 300^\circ\)**:
   Using the definition of secant:
   \[
   \sec 300^\circ = \frac{1}{\cos 300^\circ} = \frac{1}{\frac{1}{2}} = 2
   \]

So, the exact value of \(\sec 300^\circ\) is:
\[
\sec 300^\circ = 2
\]

Would you like more details or have any questions on this? 

### Related Questions
1. What is the value of \(\sec 60^\circ\)?
2. How do we determine reference angles in different quadrants?
3. What is the exact value of \(\sec 240^\circ\)?
4. How do we find the exact value of \(\cos 330^\circ\)?
5. What is the value of \(\sec 0^\circ\)?

**Tip:** Remember that in trigonometry, secant, cosecant, and cotangent can be calculated using their reciprocal definitions with sine, cosine, and tangent, respectively.

Find the exact value of sec 300° with a clear step-by-step explanation. Learn about the secant function, how to use reference angles, and key trigonometric identities. This guide is perfect for students in Grades 9-12.

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