To find the value of tan-1(13), we are looking for an angle in degrees whose tangent is equal to 13. The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.
However, it’s important to note that the tangent function can take on any real value; thus, there will be an angle corresponding to a tangent value of 13. Generally, the value of tan-1(x) (also known as arctan) yields a principal value in the range of -90° to 90°.
Using a calculator or suitable software, we can find the value:
- tan-1(13) ≈ 85.0°
This means that the angle whose tangent is 13 is approximately 85.0 degrees. This angle is very close to 90 degrees, confirming that the tangent function is indeed increasing within this range.