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NSW · Maths Extension 1
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NSWMaths Extension 1Trigonometric Functions (ME-T1, T2, T3)

Quick questions on Inverse trigonometric functions: definitions, principal branches, domains, ranges and graphs

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the identities you are expected to know?
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The complementary identity links arcsin⁡\arcsin and arccos⁡\arccos:
What is composing a trig function with its inverse?
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Applying a function then its inverse cancels, provided you start in the right set:
What is out-of-domain input?
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arcsin⁡(2)\arcsin(2) is undefined because 2∉[−1,1]2 \not\in [-1, 1]. Always check the argument is in range (for arcsin⁡\arcsin, arccos⁡\arccos).
What is sign errors in the arctan⁡\arctan sum identity?
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arctan⁡x+arctan⁡y=arctan⁡ ⁣(x+y1−xy)\arctan x + \arctan y = \arctan\!\left( \frac{x + y}{1 - x y} \right) requires xy<1x y < 1. If xy>1x y > 1 and both positive, add π\pi; if both negative, subtract π\pi.

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