Principal values versus a complete angle set
8 written marks
In this question all angles are in radians. Exact answers are required.
Part a · 3 marks
Evaluate \(\displaystyle \sin^{-1}(\sin\frac\pi3)\), \(\displaystyle \sin^{-1}(\sin\frac{2\pi}{3})\) and \(\displaystyle \sin^{-1}(\sin\frac{7\pi}{6})\).
Part b · 3 marks
Solve \(\displaystyle \tan x=\tan(\frac{5\pi}{4})\) for \(-\pi\le x\lt 2\pi\).
Part c · 2 marks
A student writes \(\displaystyle \sin^{-1}(\frac12)=2\). Explain the notation error and give the correct principal value.
Complete-answer checking, worked solutions and indicative written criteria.
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