Master Your Health: Understanding BMI
Body Mass Index (BMI) is a simple but powerful tool for assessing your health. Learn what your numbers mean and how to calculate them.
Feb 11, 2026
tan(θ) =
1
Common Angles
How to Use This Calculator
1
Enter Values
Fill in the required fields with your numbers.
2
Calculate
Click calculate or see results update in real time.
3
Read Results
View detailed breakdowns and explanations below.
📘 Definition
In a right triangle, tangent is defined as:
tan(θ) = opposite / adjacent = sin(θ) / cos(θ)
On the unit circle, tan(θ) is the slope of the line from the origin to the point at angle θ.
🎓 Key Values
- tan(0°) = 0
- tan(30°) = 1/√3 ≈ 0.577
- tan(45°) = 1
- tan(60°) = √3 ≈ 1.732
- tan(90°) = Undefined
- tan(180°) = 0
- tan(270°) = Undefined
💡 Properties
- Periodic: tan(θ + 180°) = tan(θ)
- Odd Function: tan(-θ) = -tan(θ)
- Range: All real numbers (-∞, ∞)
- Derivative: d/dθ[tan(θ)] = sec²(θ)
- Undefined: When cos(θ) = 0 (at 90°, 270°, etc.)
🚀 Applications
- Surveying: Calculating heights and distances
- Navigation: Bearing and slope calculations
- Physics: Inclined planes and projectile motion
- Engineering: Structural angles and gradients
- Calculus: Integration and differentiation
⚡ Tangent Identities
- tan(θ) = 1/cot(θ)
- 1 + tan²(θ) = sec²(θ)
- tan(A + B) = (tan A + tan B) / (1 - tan A · tan B)
Frequently Asked Questions
Popular Categories
Browse calculators by topic
From Our Blog
Related articles and insights
Percentages Made Easy: A Practical Guide
From discounts to tips, percentages are everywhere. Master the basics of percentage increase and decrease with this easy guide.
Feb 11, 2026
The Magic of Compound Interest
Albert Einstein reportedly called it the eighth wonder of the world. Discover how compound interest can grow your wealth exponentially over time.
Feb 11, 2026