The cotangent function, represented as cot(θ), where θ is an angle, helps in determining the ratio of the adjacent side to the opposite side of a right-angled triangle. It is the reciprocal of the tangent function, making it indispensable in scenarios where angles and side lengths are involved, such as in the construction, navigation, and design industries.
Formula of Cot on Calculator
The fundamental formula for calculating cotangent is straightforward:
cot(θ) = 1 / tan(θ)
Where θ represents the angle in degrees, cot(θ) is the cotangent of angle θ, and tan(θ) is the tangent of angle θ. This simple formula is a powerful tool in trigonometry, enabling the calculation of an angle’s cotangent by simply knowing its tangent.
General Table for Common Cotangent Values
For ease of reference and to aid in quick calculations, below is a table of common angles and their cotangent values. This table serves as a handy guide for those who need to solve problems without the use of a calculator or wish to verify their calculations.
| Angle (θ) | Cotangent (cot(θ)) |
|---|---|
| 0° | Undefined |
| 30° | √3 |
| 45° | 1 |
| 60° | 1/√3 |
| 90° | 0 |
Example of Cot on Calculator
To demonstrate how to use the cotangent function, consider finding the cotangent of a 45° angle. Using our formula:
cot(45°) = 1 / tan(45°) = 1
This means the cotangent of a 45° angle is 1, indicating that at this angle, the length of the adjacent side is equal to the length of the opposite side.
Most Common FAQs
A1: Use the cotangent formula along with the known tangent values or refer to a cotangent table for common angles.
A2: Cotangent is the reciprocal of tangent. While tangent represents the ratio of the opposite side to the adjacent side. Cotangent represents the ratio of the adjacent side to the opposite side.
A3: Yes, cotangent values can be negative depending on the angle. Reflecting the orientation and direction of the angle in different quadrants.
