| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Topic | Standard trigonometric equations |
| Type | Solve using given identity |
| Difficulty | Standard +0.3 Part (i) is a straightforward compound angle formula application requiring one standard identity. Part (ii) uses the result to solve a trigonometric equation over a full period, requiring systematic case-work but following a standard method. The question is slightly easier than average due to the scaffolding provided and routine nature of both parts. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Show that $\sin(2\theta + \frac{1}{2}\pi) = \cos 2\theta$. [2]
\item Hence solve the equation $\sin 3\theta = \cos 2\theta$ for $0 \leq \theta \leq 2\pi$. [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q13 [8]}}