C# - Why is Math.Atan(1) != anything near 45

Question

There is another post here about Atan but I dont see any relevant answers:

C# - Why Math.Atan(Math.Tan(x)) != x?

Isn't Math.Atan the same as tan-1? On my calculator I do:

tan-1(1) and i get 45.

tan(45) = 1

In C#:

Math.Atan(1) = 0.78539816339744828 // nowhere near the 45.

Math.Tan(45) = 1.6197751905438615 //1 dp over the < Piover2.

Whats happening here?

Answer 1

C# is treating the angles as radians; your calculator is using degrees.

Answer 2

Atan(1) is equal to π/4. This is the correct value when working in radians. The same can be said of the other calculations in the library.

Feel free to convert the values:

double DegreeToRadian(double angle) { return Math.PI * angle / 180.0;   }
double RadianToDegree(double angle) { return angle * (180.0 / Math.PI); }

This means that 45 radians is equal to about 2578.31008 degrees, so the tangent you are looking for should be better expressed as tan(π/4) or if you don't mind "cheating": Math.Tan(Math.Atan(1)); // ~= 1. I'm fairly confident that had you tried that yourself, you'd have realized something reasonable was happening, and might have stumbled upon how radians relate to degrees.