| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Standard +0.3 This is a standard two-part harmonic form question requiring the R cos(θ + α) transformation followed by solving a trigonometric equation. While it involves multiple steps (finding R and α using Pythagorean identity and tan, then solving in a given range), these are well-practiced C3 techniques with no novel insight required. Slightly above average difficulty due to the range consideration and multiple solutions, but remains a textbook exercise. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Express $4 \cos \theta - \sin \theta$ in the form $R \cos(\theta + \alpha)$, where $R > 0$ and $0° < \alpha < 90°$. [3]
\item Hence solve the equation $4 \cos \theta - \sin \theta = 2$, giving all solutions for which $-180° < \theta < 180°$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [8]}}