| 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 C3 harmonic form question with straightforward application of the R sin(θ + α) method followed by routine equation solving. Part (i) requires finding R and α using standard formulas (R = √13, tan α = 2/3), and part (ii) involves solving a simple trigonometric equation with two solutions in the given range. While it requires multiple steps and careful angle work, it follows a well-practiced textbook procedure with no novel insight needed, making it slightly easier than average. |
| 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 $3 \sin \theta + 2 \cos \theta$ in the form $R \sin(\theta + \alpha)$, where $R > 0$ and $0° < \alpha < 90°$. [3]
\item Hence solve the equation $3 \sin \theta + 2 \cos \theta = \frac{5}{2}$, giving all solutions for which $0° < \theta < 360°$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [8]}}