As pointed out here https://github.com/JuliaIntervals/IntervalArithmetic.jl/pull/621#discussion_r1469320240, the function `_quadrant` used internally for trigonometric functions may yield wrong results. See https://github.com/JuliaIntervals/IntervalArithmetic.jl/pull/621#discussion_r1469423662 for a proposal to fix the issue (at least partially). Also, this issue can be related to #129 on the implementation of `mod` for intervals (see also PR #145 and #178).