arctan23

arctan23 refers to the value of the inverse tangent function at 23, written as arctan(23). The arctangent function, arctan x, yields the unique angle θ in the interval (-π/2, π/2) such that tan θ = x. Therefore arctan(23) is a positive angle whose tangent is 23.

The principal value of arctan(23) is approximately 1.5273457 radians, which is about 87.56 degrees. As a general property, arctan x increases with x and approaches π/2 as x grows large; in particular, arctan(23) is close to π/2 but remains strictly less than it.

One useful identity for computing arctan(23) is arctan(23) = π/2 − arctan(1/23). This follows from the complementary relationship of tangent for angles in the first quadrant and is handy because 1/23 ≈ 0.0435 lies in a range where the arctan series or approximations are more stable. In practice, arctan(23) can be evaluated numerically by standard methods, such as series expansions for small arguments after the transformation above, or by calculator and software routines.

In mathematics, arctan(23) has no simple closed-form expression in terms of elementary constants. It is commonly encountered in problems involving steep slopes, angle calculations from a given tangent value, or trigonometric models where a large tangent ratio is involved. The notation arctan23 is a shorthand for arctan(23) and is read as “arctangent of twenty-three.”