A quadratic range inside a trigonometric range
8 written marks
Let \(f(x)=2\sin^2x-3\sin x+1\) on \(0\le x\lt 2\pi\).
Part a · 3 marks
Find every zero of \(f\).
Part b · 3 marks
Find the range of \(f\) using a quadratic in \(u=\sin x\). No calculus is required.
Part c · 2 marks
How many distinct solutions does \(\displaystyle f(x)= - \frac{1}{8}\) have? Explain why this differs from part (a).
Complete-answer checking, worked solutions and indicative written criteria.
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