📐 Cotangent Calculator
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📌 Understanding Cotangent Calculation
The cotangent function calculates the ratio of the adjacent side to the opposite side in a right-angled triangle. The formula is:
- cot(θ) = Adjacent / Opposite
- In terms of sine and cosine, cot(θ) = cos(θ) / sin(θ).
📌 Example Calculations
| Angle (Degrees) | cot(θ) |
|---|---|
| 30° | 1.7321 |
| 45° | 1 |
| 60° | 0.5774 |
| 90° | 0 |
🔧 Practical Applications of Cotangent Function
1. Engineering & Physics: Used in wave mechanics and periodic motion.
2. Surveying & Architecture: Helps in structure design and slope measurement.
3. Navigation & Astronomy: Essential in calculating angular distances.
❓ FAQs
Q1: How do I calculate cotangent?
✅ Use the formula cot(θ) = cos(θ) / sin(θ)
Q2: What is the cotangent of 45°?
✅ cot(45°) = 1
Q3: Can cotangent be undefined?
✅ Yes, cotangent is undefined at 0° and 180° because sin(θ) = 0 at these points.
Q4: Where is the cotangent function commonly used?
✅ It is widely used in **engineering, physics, and surveying**.
Q5: Why is the cotangent function important?
✅ It helps in **solving real-world problems related to angles, heights, and gradients**.