| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Session | Specimen |
| 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 harmonic form question requiring routine application of R cos(θ + α) = R cos θ cos α - R sin θ sin α, followed by solving a straightforward trigonometric equation. The technique is well-practiced in C3/C4, though the double angle and range require careful attention to multiple solutions. |
| 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}
\item (a) Express $5 \cos 2 \theta - 12 \sin 2 \theta$ in the form $R \cos ( 2 \theta + \alpha )$, where $R > 0$ and $0 < \alpha < 90 ^ { \circ }$ Give the value of $\alpha$ to 2 decimal places.\\
(b) Hence solve, for $0 \leqslant \theta < 180 ^ { \circ }$, the equation
\end{enumerate}
$$5 \cos 2 \theta - 12 \sin 2 \theta = 10$$
giving your answers to 1 decimal place.\\
\hfill \mbox{\textit{Edexcel C34 Q1 [8]}}