The value of \(\cot(-5\pi/6)\) can be calculated as follows:

1. **Understanding the angle**: 
   \[
   -5\pi/6 \text{ is in the third quadrant since it's equivalent to } \pi - (-5\pi/6) = \pi/6 \text{ radians}.
   \]
   In the third quadrant, cotangent is positive, because \(\cot(\theta) = \frac{1}{\tan(\theta)}\), and both sine and cosine are negative, making their ratio positive.

2. **Reference angle**: 
   The reference angle for \(-5\pi/6\) is \(\pi/6\).

3. **Cotangent of the reference angle**: 
   \[
   \cot(\pi/6) = \sqrt{3}
   \]

4. **Sign**: 
   Since the cotangent function is positive in the third quadrant, the value of \(\cot(-5\pi/6)\) is the same as \(\cot(\pi/6)\).

Thus, \(\cot(-5\pi/6) = \sqrt{3}\).

---

Do you need further details or have any questions?

Here are five related questions:
1. What is the value of \(\tan(-5\pi/6)\)?
2. How do you calculate \(\sin(-5\pi/6)\)?
3. What is the general formula for cotangent in different quadrants?
4. Can you derive cotangent from sine and cosine?
5. How do you convert angles between radians and degrees?

**Tip**: Remember that cotangent is the reciprocal of tangent, i.e., \(\cot(\theta) = \frac{1}{\tan(\theta)}\).

Learn how to calculate the cotangent of -5π/6 using trigonometric principles. This problem explores cotangent function behavior in different quadrants, reference angles, and reciprocal identities. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation