Moderate -0.3 This is a standard C4 harmonic form question with routine application of the R sin(θ - α) formula. Students follow a well-practiced algorithm (find R using Pythagoras, find α using tan), then simply add/subtract R from 1. The method is mechanical with no problem-solving required, making it slightly easier than average.
1 Express \(2 \sin \theta - 3 \cos \theta\) in the form \(R \sin ( \theta - \alpha )\), where \(R\) and \(\alpha\) are constants to be determined, and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
Hence write down the greatest and least possible values of \(1 + 2 \sin \theta - 3 \cos \theta\).
1 Express $2 \sin \theta - 3 \cos \theta$ in the form $R \sin ( \theta - \alpha )$, where $R$ and $\alpha$ are constants to be determined, and $0 < \alpha < \frac { 1 } { 2 } \pi$.
Hence write down the greatest and least possible values of $1 + 2 \sin \theta - 3 \cos \theta$.
\hfill \mbox{\textit{OCR C4 Q1 [6]}}