I was referring to direct use of the inverse tangent rather than using a formula for inverse sine or cosine.

In real world engineering and scientific problems, you are almost always working with triangles or Cartesian coordinates.
  • When working with triangles, the sine of an angle is the ratio of the opposite side and the hypotenuse, while cosine sine is the ratio of the adjacent side and the hypotenuse. The tangent is the ratio of the opposite and adjacent sides. If you know the sides of the triangle, you can always use inverse tangent to determine angles, making it unnecessary to use inverse sine or cosine.
  • When working with Cartesian coordinates and a point (X, Y), the tangent is Y/X. Inverse tangent of (Y/X) can be used instead of inverse cosine [ X / Sqr(X^2 + Y^2) ].
I have dealt with a lot of real world problems and have always been able to use inverse tangent directly, except for some problems assigned by a professor.