| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Multiple angle equations |
| Difficulty | Standard +0.3 This is a standard C3 trigonometry question testing cosecant and cotangent equations. Part (a)(i) is routine recall (2 marks), part (a)(ii) requires substitution using the identity cot²θ + 1 = cosec²θ to form a quadratic in cosec, then solving with domain considerations (6 marks), and part (b) tests understanding of function transformations. While multi-step, these are textbook techniques with no novel insight required, making it slightly easier than average overall. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Solve the equation $\cosec \theta = -4$ for $0° < \theta < 360°$, giving your answers to the nearest 0.1°. [2]
\item Solve the equation
$$2\cot^2(2x + 30°) = 2 - 7\cosec(2x + 30°)$$
for $0° < x < 180°$, giving your answers to the nearest 0.1°. [6]
\end{enumerate}
\item Describe a sequence of two geometrical transformations that maps the graph of $y = \cosec x$ onto the graph of $y = \cosec(2x + 30°)$. [4]
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2011 Q4 [12]}}