| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve factored trig equation |
| Difficulty | Moderate -0.3 This is a straightforward C2 trigonometry question with three routine parts: (a) identifying a horizontal stretch transformation (standard bookwork), (b) solving a simple equation tan(x/2)=3 using inverse tan and periodicity, and (c) solving a factored equation requiring basic knowledge of when cos θ = 0 and tan θ = 3. All parts are standard textbook exercises requiring recall and direct application rather than problem-solving, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
8
\begin{enumerate}[label=(\alph*)]
\item Describe the single geometrical transformation by which the curve with equation $y = \tan \frac { 1 } { 2 } x$ can be obtained from the curve $y = \tan x$.
\item Solve the equation $\tan \frac { 1 } { 2 } x = 3$ in the interval $\mathbf { 0 } < \boldsymbol { x } < \mathbf { 4 } \boldsymbol { \pi }$, giving your answers in radians to three significant figures.
\item Solve the equation
$$\cos \theta ( \sin \theta - 3 \cos \theta ) = 0$$
in the interval $0 < \theta < 2 \pi$, giving your answers in radians to three significant figures.\\
(5 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2006 Q8 [11]}}