Standard +0.3 This is a standard trigonometric equation requiring the Pythagorean identity to convert to a quadratic in sin x, then solving for exact values within a given range. While it requires multiple steps (substitution, factoring, finding angles), these are routine A-level techniques with no novel insight needed, making it slightly easier than average.
4 In this question you must show detailed reasoning.
Determine the exact solutions of the equation \(2 \cos ^ { 2 } x = 3 \sin x\) for \(0 \leqslant x \leqslant 2 \pi\).
For getting a 3-term quadratic on the same side in a single trig ratio (not dep on M1)
\(\sin x = \frac{1}{2}\)
A1
BC, ignore second value if presented
\(\frac{\pi}{6}\)
A1
First angle correct and in radians
\(\frac{5\pi}{6}\)
B1
FT (\(\pi -\) their first angle) OR (\(180 -\) their first angle) dep on first M1. If further solutions in range B0
# Question 4:
| Answer | Mark | Guidance |
|--------|------|----------|
| $2(1 - \sin^2 x) = 3\sin x$ | M1 | |
| $2\sin^2 x + 3\sin x - 2\ [=0]$ | M1 | For getting a 3-term quadratic on the same side in a single trig ratio (not dep on M1) |
| $\sin x = \frac{1}{2}$ | A1 | BC, ignore second value if presented |
| $\frac{\pi}{6}$ | A1 | First angle correct and in radians |
| $\frac{5\pi}{6}$ | B1 | FT ($\pi -$ their first angle) OR ($180 -$ their first angle) dep on first M1. If further solutions in range B0 |
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4 In this question you must show detailed reasoning.\\
Determine the exact solutions of the equation $2 \cos ^ { 2 } x = 3 \sin x$ for $0 \leqslant x \leqslant 2 \pi$.
\hfill \mbox{\textit{OCR MEI Paper 3 2022 Q4 [5]}}