Inverse Trig: Domain & Range Traps
Test your command of the domains and ranges of the six inverse trigonometric functions, where most JEE Main mistakes are made before any calculation starts.
Fourteen questions cover the range of each inverse function, the open and closed endpoints, the values that can never appear, when arcsin(sin x) and arccos(cos x) return x unchanged, and the conditions attached to the standard identities.
Includes the ab < 1 condition on the arctan addition formula, which is skipped far more often than it is applied.
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Sample questions3 of 14 shown
Q1
A student writes: "If x is large enough, then arctan x = π/2." Which statement corrects him?
Q2
Which of the following can NEVER be the value of arcsin x for any admissible x?
Q3
A student claims arccot x = 0 for some very large x. Which value is actually NOT in the range of arccot x?
What This Quiz Covers
- Ranges of all six inverse functions
- Open against closed endpoints
- arcsin(sin x) = x only on [−π/2, π/2]
- arccos(cos x) = x only on [0, π]
- arcsin x + arccos x = π/2 and its domain
- The ab < 1 condition on arctan addition
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