Moderate -0.3 This is a standard C4 harmonic form question requiring the R sin(x + α) transformation using R² = a² + b² and tan α = b/a, followed by finding a maximum by setting the sine term equal to 1. While it involves multiple steps, it's a routine textbook exercise with well-practiced techniques and no novel problem-solving required, making it slightly easier than average.
Express \(3\sin x + 2\cos x\) in the form \(R\sin(x + \alpha)\), where \(R > 0\) and \(0 < \alpha < \frac{\pi}{2}\).
Hence find, correct to 2 decimal places, the coordinates of the maximum point on the curve \(y = f(x)\), where
$$f(x) = 3\sin x + 2\cos x, \quad 0 < x < \pi.$$ [7]
Express $3\sin x + 2\cos x$ in the form $R\sin(x + \alpha)$, where $R > 0$ and $0 < \alpha < \frac{\pi}{2}$.
Hence find, correct to 2 decimal places, the coordinates of the maximum point on the curve $y = f(x)$, where
$$f(x) = 3\sin x + 2\cos x, \quad 0 < x < \pi.$$ [7]
\hfill \mbox{\textit{OCR MEI C4 2012 Q3 [7]}}