Understanding Arctan (Inverse Tangent)
The arctangent function, written as arctan or tan⁻¹, is the inverse of the tangent function. It takes a ratio and returns the corresponding angle.
Formula
For a single value:
[\text{arctan}(x) = \theta]
Where θ is the angle whose tangent equals x.
For the sum of two arctangent values (as this calculator computes):
[\text{Result} = \text{arctan}(x) + \text{arctan}(y)]
Example Calculation
Let's calculate arctan(0.5) in degrees:
- Input: x = 0.5
- Calculate: arctan(0.5) = 0.4636 radians
- Convert to degrees: 0.4636 × (180/π) = 26.57 degrees
If we wanted to add another arctangent, say arctan(0):
- arctan(0.5) = 26.57 degrees
- arctan(0) = 0 degrees
- Sum = 26.57 degrees
Common Uses
- Engineering: Finding angles from slopes or gradients
- Navigation: Calculating bearing angles from coordinate differences
- Physics: Determining angles in projectile motion
- Computer Graphics: Calculating rotation angles from coordinate pairs