| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Topic | Reciprocal Trig & Identities |
| Type | Sketch reciprocal function graphs |
| Difficulty | Moderate -0.3 Part (a) is a standard sketch of sec θ requiring knowledge of reciprocal trig functions and their asymptotes. Part (b) involves solving sec θ = cosec θ, which simplifies to sin θ = cos θ, a routine equation. Both parts test fundamental understanding with straightforward application, making this slightly easier than average but not trivial. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
**Question 4:**
**(i)** [Sketch of $y = \sec\theta$] **B1** (Award for 3 branches of roughly correct shape with two asymptotes)
**(ii)** $\frac{1}{\cos\theta} = \frac{1}{\sin\theta}$ **M1** (Allow equivalent methods)
$\tan\theta = 1$ **M1**
$\frac{\pi}{4}$ or $45°$ **A1**
$\frac{5}{4}\pi$ **A1** (A0 if more angles given or if in degrees)
**Total: 5 marks**4
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = \sec \theta$ for $0 \leqslant \theta \leqslant 2 \pi$.
\item Solve $\sec \theta = \operatorname { cosec } \theta$ for $0 \leqslant \theta \leqslant 2 \pi$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2018 Q4 [5]}}