| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Moderate -0.3 This is a standard two-part question on the R-formula (harmonic form) with straightforward application. Part (a) requires routine use of R cos α = 4, R sin α = 3 to find R = 5 and α ≈ 36.87°. Part (b) is a direct substitution leading to a single inverse sine calculation. The question is slightly easier than average because it follows a completely standard template with no complications or novel elements. |
| 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=(\alph*)]
\item Express $3 \sin x - 4 \cos x$ in the form $R \sin(x - \alpha)$, where $R > 0$ and $0° < \alpha < 90°$. Give the value of $\alpha$ correct to 4 significant figures. [3]
\item Hence solve the equation $3 \sin x - 4 \cos x = 2$ for $0° < x < 90°$, giving your answer correct to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2023 Q2 [5]}}