Inverse trig functions
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Flip to reveal answersWhy does sine need a restricted domain to have an inverse?
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All 8 Flashcards — Inverse trig functions
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Question
Why does sine need a restricted domain to have an inverse?
Answer
Over all reals sine repeats, so sin x = c has many solutions. Restricting to [−π/2, π/2] makes it one-to-one, so it can be reversed.
Question
Domain and range of arcsin x?
Answer
Domain [−1, 1], range [−π/2, π/2].
Question
Domain and range of arccos x?
Answer
Domain [−1, 1], range [0, π].
Question
Domain and range of arctan x?
Answer
Domain all real numbers, range (−π/2, π/2) (open).
Question
Exact value of arctan(√3)?
Answer
π/3, since tan(π/3) = √3 and π/3 is in (−π/2, π/2).
Question
Exact value of arccos(−1/2)?
Answer
2π/3 (cosine is −1/2 there, and 2π/3 is in [0, π]).
Question
Simplify cos(arcsin x).
Answer
Let θ = arcsin x ⇒ sin θ = x; cos θ = √(1 − x²) (non-negative on [−π/2, π/2]).
Question
How do you sketch y = arcsin x from y = sin x?
Answer
Take the rising piece of sine on [−π/2, π/2] and reflect it in the line y = x.
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Full study notes for Inverse trig functions
Topic 3.9 hub
Reciprocal & inverse trig (HL only)
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