| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Range of squared harmonic expression |
| Difficulty | Standard +0.3 This is a standard C3 harmonic form question with routine steps: (a) uses the R sin(θ+α) formula requiring Pythagoras and arctan, (b) applies double angle identities, and (c) connects parts (a) and (b) to find a maximum. All techniques are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
\begin{enumerate}[label=(\alph*)]
\item Express $1.5 \sin 2x + 2 \cos 2x$ in the form $R \sin (2x + \alpha)$, where $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$, giving your values of $R$ and $\alpha$ to 3 decimal places where appropriate. [4]
\item Express $3 \sin x \cos x + 4 \cos^2 x$ in the form $a \cos 2x + b \sin 2x + c$, where $a$, $b$ and $c$ are constants to be found. [2]
\item Hence, using your answer to part (a), deduce the maximum value of $3 \sin x \cos x + 4 \cos^2 x$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q16 [8]}}