| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | October |
| Marks | 7 |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Standard +0.3 This is a standard two-part question on the R-formula (harmonic form) followed by solving a trigonometric equation. Part (i) requires routine application of R cos α = 7, R sin α = 24 to find R = 25 and α ≈ 16.3°. Part (ii) involves solving 25 sin(θ + α) = 12, which is straightforward once the form is established. This is a textbook exercise testing technique rather than problem-solving, making it slightly easier than average. |
| 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=(\roman*)]
\item Express $24 \sin \theta + 7 \cos \theta$ in the form $R \sin(\theta + \alpha)$, where $R > 0$ and $0° < \alpha < 90°$.
[3]
\item Hence solve the equation $24 \sin \theta + 7 \cos \theta = 12$ for $0° < \theta < 360°$.
[4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q7 [7]}}