Tan Calculator for Degrees
Introduction & Importance
The tangent function, often denoted as ‘tan’, is a fundamental trigonometric function that measures the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle. Understanding and calculating tangent is crucial in various fields, including mathematics, physics, engineering, and more.
How to Use This Calculator
- Enter the angle in degrees.
- Click the ‘Calculate’ button.
- View the result below the calculator.
Formula & Methodology
The tangent of an angle in degrees can be calculated using the formula:
tan(degrees) = (sin(degrees) / cos(degrees))
Where ‘sin’ and ‘cos’ are the sine and cosine functions respectively, which can be calculated using the following formulas:
sin(degrees) = sin(degrees * (π / 180))
cos(degrees) = cos(degrees * (π / 180))
Real-World Examples
Example 1: Angle of 45 degrees
In a right-angled triangle, if the angle opposite the adjacent side is 45 degrees, the tangent of this angle is 1.
Example 2: Angle of 30 degrees
In a 30-60-90 triangle, the tangent of the 30-degree angle is √3/3.
Example 3: Angle of 60 degrees
In a 30-60-90 triangle, the tangent of the 60-degree angle is √3.
Data & Statistics
| Angle (degrees) | Tangent |
|---|---|
| 0 | 0 |
| 30 | √3/3 |
| 45 | 1 |
| 60 | √3 |
| 90 | undefined |
| Angle (degrees) | Tangent |
|---|---|
| 15 | 0.2679 |
| 33 | 0.6547 |
| 47 | 1.1918 |
| 65 | 2.1658 |
| 87 | 4.7124 |
Expert Tips
- Remember that the tangent function is undefined for angles of 90 degrees and any angle coterminal with 90 degrees.
- To find the tangent of an angle in degrees, you can use a scientific calculator or a calculator with trigonometric functions.
- Inverse tangent (arctan) can be used to find the angle given the tangent value.
Interactive FAQ
What is the tangent of 0 degrees?
The tangent of 0 degrees is 0.
What is the tangent of 90 degrees?
The tangent of 90 degrees is undefined.
How can I find the angle given the tangent value?
You can use the inverse tangent (arctan) function to find the angle given the tangent value.
For more information, see the Math is Fun guide on tangent and the Tangent Calculator by CalculatorSoup.