asec(): Finding an Angle from a Secant

asec() returns a principal angle whose secant is the supplied value. Secant is the reciprocal of cos(), so asec is useful when a formula gives a reciprocal cosine ratio directly.

Domain and branch choice

For a real result, the input must have magnitude at least one: x ≤ −1 or x ≥ 1. Zero is impossible because secant is never zero. asec returns one conventional representative even though secant repeats, so its result should be interpreted as a principal value rather than every solution.

The relationship asec(x) = acos(1/x) is useful for intuition and checking. However, dividing by a small value is unstable and x must not be zero. Use abs() to validate magnitude, and use acos() when your quantity is already a cosine rather than a secant.

Applications and verification

Reciprocal trigonometric functions appear in integrals, geometry, and some engineering formulas. Verify a valid calculation by applying sec() to the result. Keep all angles in radians while calculating.

If a direction comes from two coordinates, atan2() is often more robust because it preserves the quadrant without reciprocal conversion. Choose asec when secant is genuinely the known measurement.