| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Given sin/cos/tan, find other expressions |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard trigonometric identities. Part (a) uses basic Pythagorean identity and double angle formula with given values. Part (b) requires finding sin β and cos β from tan β, then applying the compound angle formula—all routine techniques with no novel problem-solving required. Slightly easier than average due to the scaffolded structure and standard methods. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae |
2 The acute angles $\alpha$ and $\beta$ are given by $\tan \alpha = \frac { 2 } { \sqrt { 5 } }$ and $\tan \beta = \frac { 1 } { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Show that $\sin \alpha = \frac { 2 } { 3 }$, and find the exact value of $\cos \alpha$.
\item Hence find the exact value of $\sin 2 \alpha$.
\end{enumerate}\item Show that the exact value of $\cos ( \alpha - \beta )$ can be expressed as $\frac { 2 } { 15 } ( k + \sqrt { 5 } )$, where $k$ is an integer.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2013 Q2 [8]}}