| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Derive triple angle then solve equation |
| Difficulty | Challenging +1.2 Part (i) is a standard trigonometric identity derivation using compound angle formulas (routine for C3). Part (ii) requires recognizing the triple angle formula from (i) and finding maximum value, which is moderately challenging. Part (iii) involves product-to-sum formulas and solving a more complex trigonometric equation with restricted domain, requiring several non-trivial steps. Overall, this is harder than average C3 questions due to the multi-step reasoning and connections between parts, but still within standard A-level techniques. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item By first writing $\sin 3\theta$ as $\sin(2\theta + \theta)$, show that
$$\sin 3\theta = 3 \sin \theta - 4 \sin^3 \theta.$$ [4]
\item Determine the greatest possible value of
$$9 \sin(\frac{10}{3}\alpha) - 12 \sin^3(\frac{10}{3}\alpha),$$
and find the smallest positive value of $\alpha$ (in degrees) for which that greatest value occurs. [3]
\item Solve, for $0° < \beta < 90°$, the equation $3 \sin 6\beta \cos 2\beta = 4$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q9 [13]}}