Inverse Trigonometric Functions
Sine hits every value in its range infinitely often, so its inverse can only exist by contract: arcsin answers from the right half circle, arccos from the top half, arctan from one tangent branch. Each returns exactly one angle, and an angle outside the contract is wrong even when its sine or cosine matches.
Two mistakes own this topic. The first is range blindness: reporting two answers, or a coterminal answer, where the inverse function is only allowed its one. The second is the notation collision: reading the superscript in the inverse notation as an exponent and turning an inverse function into a reciprocal, which is cosecant, a different function with different values. Both are drilled head-on in the lesson.
The work
3 ways in · any order
Lesson
Inverse Trigonometric Functions
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One question, one answer: the lesson builds the three restricted ranges, evaluates exact values inside them, splits inverse notation from reciprocals with a numeric showdown, and walks the one-way round trips. Ten scenarios enforce the contract.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 3.9 misconceptions: answers that wander outside the inverse ranges, and the superscript read as a reciprocal. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.