反三角函数的基本公式包括:
arcsin(-x) = -arcsinx
arccos(-x) = π - arccosx
arctan(-x) = -arctanx
arccot(-x) = π - arccotx
arcsinx + arccosx = π/2 = arctanx + arccotx
sin(arcsinx) = x = cos(arccosx) = tan(arctanx) = cot(arccotx)
当 x ∈ [-π/2, π/2] 时, arcsin(sinx) = x
当 x ∈ [0, π] 时, arccos(cosx) = x
当 x ∈ (-π/2, π/2) 时, arctan(tanx) = x
当 x ∈ (0, π) 时, arccot(cotx) = x
x > 0, arctanx = arctan(1/x)
若 (arctanx + arctany) ∈ (-π/2, π/2), 则 arctanx + arctany = arctan(x + y / (1 - xy))
这些公式可以帮助你在处理涉及反三角函数的数学问题时,更有效地进行计算和推导。