what about B) tan(- 5pi/60 and C) sec( -7pi/3)

Let's solve both problems one by one:

### B) \( \tan\left(-\frac{5\pi}{60}\right) \)

First, simplify the angle:

\[
-\frac{5\pi}{60} = -\frac{\pi}{12}
\]

Now, evaluate \( \tan\left(-\frac{\pi}{12}\right) \). Using the fact that \( \tan(-x) = -\tan(x) \), we have:

\[
\tan\left(-\frac{\pi}{12}\right) = -\tan\left(\frac{\pi}{12}\right)
\]

From known trigonometric values, \( \tan\left(\frac{\pi}{12}\right) = 2 - \sqrt{3} \), so:

\[
\tan\left(-\frac{\pi}{12}\right) = -(2 - \sqrt{3}) = \sqrt{3} - 2
\]

Thus:

\[
\tan\left(-\frac{5\pi}{60}\right) = \sqrt{3} - 2
\]

---

### C) \( \sec\left(-\frac{7\pi}{3}\right) \)

First, reduce the angle \( -\frac{7\pi}{3} \) to a standard position within \( [0, 2\pi] \):

\[
-\frac{7\pi}{3} + 2\pi = -\frac{7\pi}{3} + \frac{6\pi}{3} = -\frac{\pi}{3}
\]

Now, use the property \( \sec(-x) = \sec(x) \), so:

\[
\sec\left(-\frac{\pi}{3}\right) = \sec\left(\frac{\pi}{3}\right)
\]

Since \( \sec\left(\frac{\pi}{3}\right) = 2 \), we have:

\[
\sec\left(-\frac{7\pi}{3}\right) = 2
\]

---

### Final Answers:
B) \( \tan\left(-\frac{5\pi}{60}\right) = \sqrt{3} - 2 \)

C) \( \sec\left(-\frac{7\pi}{3}\right) = 2 \)

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

Here are 5 related questions for practice:
1. What is \( \tan\left(-\frac{3\pi}{4}\right) \)?
2. How would you simplify \( \sec\left(\frac{11\pi}{6}\right) \)?
3. What is the general formula for \( \tan(-x) \)?
4. How does the secant function behave with negative angles?
5. What is \( \tan\left(\frac{7\pi}{6}\right) \)?

**Tip:** When simplifying angles in radians, always try to reduce them into the range \( [0, 2\pi] \) for easier calculation.

What about B) tan(-5pi/60) and C) sec(-7pi/3)?

Learn how to simplify and evaluate the trigonometric functions tan(-5π/60) and sec(-7π/3). This solution involves reducing angles to standard positions, using trigonometric identities, and understanding the properties of tan and sec functions. Suitable for students in Grades 10-12.

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