| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Equation with 'show that' rewriting preliminary part |
| Difficulty | Moderate -0.3 This is a straightforward C2 trigonometry question testing standard identities and equation solving. Part (a) requires simple algebraic manipulation of a trigonometric expression (2 marks). Part (b) uses the Pythagorean identity sin²x + cos²x = 1 to transform the equation, then solving a quadratic in sin x - both routine techniques for C2 level with no novel insight required. The 9 total marks reflect length rather than conceptual difficulty. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item Given that $\frac{\sin \theta - \cos \theta}{\cos \theta} = 4$, prove that $\tan \theta = 5$. [2]
\item \begin{enumerate}[label=(\roman*)]
\item Use an appropriate identity to show that the equation
$$2 \cos^2 x - \sin x = 1$$
can be written as
$$2 \sin^2 x + \sin x - 1 = 0$$ [2]
\item Hence solve the equation
$$2 \cos^2 x - \sin x = 1$$
giving all solutions in the interval $0° \leq x \leq 360°$. [5]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q8 [9]}}