Which inverse reciprocal trig function has the largest maximum?

The principal range of arccsc θ is from −π/2 to π/2, excluding 0, so its maximum is π/2. Arcsec θ has range [0, π] with π/2 excluded, so it reaches a maximum of π. Arccot θ has range (0, π): it approaches π but never reaches it, so it has no maximum. Therefore, arcsec θ has the largest maximum.

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