| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Standard trigonometric equations |
| Type | Multiple independent equations — all direct solve |
| Difficulty | Moderate -0.3 Both parts are standard trigonometric equation solving within a restricted domain. Part (i) requires the Pythagorean identity to convert to a quadratic in cos x, then solving; part (ii) uses tan 2x = -1 with angle adjustment. These are routine A-level techniques with straightforward execution and no novel problem-solving required, making them slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
Solve each of the following equations, for $0° \leqslant x \leqslant 180°$.
\begin{enumerate}[label=(\roman*)]
\item $2\sin^2 x = 1 + \cos x$. [4]
\item $\sin 2x = -\cos 2x$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q3 [8]}}