| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Transformations of trigonometric graphs |
| Difficulty | Standard +0.3 This is a standard C3 harmonic form question with three routine parts: expressing a cos + b sin in R cos(x - α) form using Pythagorean identity and tan α = b/a, describing transformations (stretch and translation), and solving a resulting equation. All techniques are textbook exercises requiring methodical application rather than insight, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)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 $5 \cos x + 12 \sin x$ in the form $R \cos(x - \alpha)$, where $R > 0$ and $0° < \alpha < 90°$. [3]
\item Hence give details of a pair of transformations which transforms the curve $y = \cos x$ to the curve $y = 5 \cos x + 12 \sin x$. [3]
\item Solve, for $0° < x < 360°$, the equation $5 \cos x + 12 \sin x = 2$, giving your answers correct to the nearest $0.1°$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q8 [11]}}