The value of cot 1 in trigonometry depends on whether '1' is interpreted as 1 radian or 1 degree. We will explore both interpretations.
Cotangent of 1 Radian
When '1' is interpreted as 1 radian, cot 1 is the cotangent of 1 radian. Radians are a unit of angular measure, where π radians equals 180 degrees. Therefore, 1 radian is approximately 57.3 degrees.
- cot(1 radian) ≈ 0.6420926159
This value can be obtained using a calculator set to radian mode or through trigonometric tables. The cotangent function, cot(x), is defined as cos(x)/sin(x). Therefore, cot(1) = cos(1)/sin(1), where the angle is in radians.
Cotangent of 1 Degree
When '1' is interpreted as 1 degree, cot 1 is the cotangent of 1 degree.
- cot(1 degree) ≈ 57.29005827
This value can be obtained using a calculator set to degree mode. It can also be approximated using the fact that for small angles (in radians), cot(x) ≈ 1/x. Converting 1 degree to radians (1 degree = π/180 radians ≈ 0.01745 radians), we have cot(1 degree) ≈ 1/(π/180) = 180/π ≈ 57.29.
Summary
| Angle | Value of cot(angle) |
|---|---|
| 1 Radian | ≈ 0.64209 |
| 1 Degree | ≈ 57.29006 |
The precise value depends on whether the angle is measured in radians or degrees. Always ensure your calculator is in the correct mode (radians or degrees) when evaluating trigonometric functions.
