| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Standard +0.3 This is a standard two-part harmonic form question requiring routine application of R-formula (finding R and α using Pythagorean identity and tan), then solving a simple equation. It's slightly above average difficulty due to the multi-step nature and need for careful angle work, but follows a well-practiced textbook procedure with no novel insight required. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
2
\begin{enumerate}[label=(\alph*)]
\item Express $\sin x - 3 \cos x$ in the form $R \sin ( x - \alpha )$, where $R > 0$ and $0 ^ { \circ } < \alpha < 90 ^ { \circ }$, giving your value of $\alpha$ to the nearest $0.1 ^ { \circ }$.
\item Hence find the values of $x$ in the interval $0 ^ { \circ } < x < 360 ^ { \circ }$ for which
$$\sin x - 3 \cos x + 2 = 0$$
giving your values of $x$ to the nearest degree.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q2 [7]}}