| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Given sin/cos/tan, find other expressions |
| Difficulty | Moderate -0.3 This is a straightforward application of standard trigonometric identities. Part (a) uses Pythagorean identity to find sin values then compute tan, requiring careful attention to quadrants. Part (b) applies the tan addition formula with basic algebraic manipulation. While it requires multiple steps and careful arithmetic, it involves only routine techniques with no problem-solving insight needed, making it slightly easier than average. |
| 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 Angle $\alpha$ is acute and $\cos \alpha = \frac { 3 } { 5 }$. Angle $\beta$ is obtuse and $\sin \beta = \frac { 1 } { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the value of $\tan \alpha$ as a fraction.\\
(1 mark)
\item Find the value of $\tan \beta$ in surd form.
\end{enumerate}\item Hence show that $\tan ( \alpha + \beta ) = \frac { m \sqrt { 3 } - n } { n \sqrt { 3 } + m }$, where $m$ and $n$ are integers.\\
(3 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q2 [6]}}