Moderate -0.3 This is a standard C4 harmonic form question with routine application of the R sin(θ - α) method followed by a straightforward equation solve. The technique is well-practiced and requires no novel insight—students learn the formula R cos α = 1, R sin α = 3, then solve R sin(θ - α) = 1 using inverse sine. Slightly easier than average due to being a textbook application with clear steps.
Express \(\sin \theta - 3 \cos \theta\) in the form \(R \sin (\theta - \alpha)\), where \(R\) and \(\alpha\) are constants to be determined, and \(0° < \alpha < 90°\).
Hence solve the equation \(\sin \theta - 3 \cos \theta = 1\) for \(0° \leqslant \theta \leqslant 360°\). [7]
Express $\sin \theta - 3 \cos \theta$ in the form $R \sin (\theta - \alpha)$, where $R$ and $\alpha$ are constants to be determined, and $0° < \alpha < 90°$.
Hence solve the equation $\sin \theta - 3 \cos \theta = 1$ for $0° \leqslant \theta \leqslant 360°$. [7]
\hfill \mbox{\textit{OCR MEI C4 Q3 [7]}}