arccosq0

Arccosq0 is not a widely standardized mathematical function. In many texts, the inverse cosine is denoted arccos(x). The term arccosq0 is sometimes used informally or as a domain-specific alias to denote arccos(q0), i.e., the inverse cosine of the quantity q0.

Definition: arccosq0 := arccos(q0). The input q0 should lie in the interval [-1,1], and the result is an angle θ in [0,π] radians.

Properties: principal value; cos(arccosq0) = q0; arccosq0 is a decreasing function of q0 on [-1,1]; derivative d/dq0 arccosq0 = -1 / sqrt(1 - q0^2).

Relations: arccosq0 is the inverse of cosine restricted to [0,π]. Inverse cosine relationships: arccos(cos θ) = θ for θ in [0,π].

Examples: q0 = 0.5 implies arccosq0 ≈ 1.0472 rad (60 degrees); q0 = -0.8 gives ≈ 2.4981 rad (143.13 degrees).

Usage and caution: In most programming languages, the inverse cosine is named acos; arccosq0 may be a user-defined alias. Always ensure q0 within [-1,1].