Numerical angles without premature rounding
8 written marks
Consider \(3\cos(2x-20^\circ)=1\) for \(-90^\circ\le x\le180^\circ\).
Part a · 2 marks
State the interval for \(u=2x-20^\circ\) and find \(\displaystyle \alpha = \cos^{- 1} (\frac{1}{3})\) to 3 decimal places.
Part b · 4 marks
Solve the equation, giving every \(x\) to 3 decimal places.
Part c · 2 marks
A student proposes the shortcut \(\cos(2x)=2\cos x\). Disprove it using \(x=60^\circ\), and explain why it cannot be used to solve part (b).
Complete-answer checking, worked solutions and indicative written criteria.
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