Find Cotangent of (alpha) at the point (0,10)

To find the cotangent of \(\alpha\) at the point \((0, 10)\), we need to understand that \(\alpha\) refers to the angle that a line (or segment) makes with the positive x-axis. However, since only a point \((0, 10)\) is given, we assume the angle \(\alpha\) is between the line from the origin \((0, 0)\) to the point \((0, 10)\) and the positive x-axis.

### Steps:

1. **Determine the Angle:**
   - The line from \((0, 0)\) to \((0, 10)\) is vertical. 
   - A vertical line has an angle of \(\alpha = 90^\circ\) (or \(\frac{\pi}{2}\) radians) with the positive x-axis.

2. **Find the Cotangent:**
   - The cotangent of an angle \(\alpha\) is defined as:
     \[
     \cot(\alpha) = \frac{1}{\tan(\alpha)}
     \]
   - For \(\alpha = 90^\circ\) (or \(\frac{\pi}{2}\) radians):
     \[
     \tan(90^\circ) \text{ is undefined (since the line is vertical), so } \cot(90^\circ) = 0
     \]

### Conclusion:
- The cotangent of the angle \(\alpha\) at the point \((0, 10)\) is \( \boxed{0} \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What is the tangent of an angle at the same point \((0, 10)\)?
2. How do you find the angle between a line and the x-axis given different points?
3. What is the significance of cotangent in trigonometry?
4. How does cotangent behave for angles larger than \(90^\circ\)?
5. What happens to trigonometric ratios as the angle approaches \(180^\circ\)?

**Tip:** Remember that the cotangent function is the reciprocal of the tangent function, and it is undefined when the angle corresponds to a vertical line (at \(90^\circ\) or \(270^\circ\)).

Discover how to find the cotangent of an angle \( \alpha \) at the point \((0, 10)\). This problem involves trigonometric concepts and the cotangent formula. Suitable for advanced high school students and anyone interested in trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation