Mixed assessment · Question 6
5 written marks
For real \(k\), consider \(\sin^2x-k\sin x=0\), with \(0\le x\lt 2\pi\).
Part a · 3 marks
Find every solution when \(\displaystyle k=-\frac12\).
Part b · 2 marks
Find all \(k\) for which the equation has exactly three distinct solutions. Justify the boundary choices.
Complete-answer checking, worked solutions and indicative written criteria.
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