| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2025 |
| Session | February |
| Marks | 6 |
| Topic | Addition & Double Angle Formulae |
| Type | Derive triple angle then solve equation |
| Difficulty | Standard +0.3 Part (a) is a standard derivation of the triple angle formula using sin(2x+x) and double angle formulae—routine A-level technique. Part (b) requires substituting the result and factorising to solve, which is straightforward once the identity is established. This is a typical textbook exercise testing formula manipulation rather than requiring novel insight, making it slightly easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
8. In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
\begin{enumerate}[label=(\alph*)]
\item Show that $\sin 3 x$ can be written in the form
$$P \sin x + Q \sin ^ { 3 } x$$
where $P$ and $Q$ are constants to be found.
\item Hence or otherwise, solve, for $0 < \theta \leq 360 ^ { \circ }$, the equation
$$2 \sin 3 \theta = 5 \sin 2 \theta$$
giving your answers, in degrees, to one decimal place as appropriate.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2025 Q8 [6]}}