| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Sketch reciprocal function graphs |
| Difficulty | Moderate -0.3 This is a straightforward C3 trigonometry question testing standard secant function knowledge. Part (i) is routine graph sketching, part (ii) requires simple inverse calculation (cos x = 1/3), and part (iii) involves converting to cos²θ = 1/5 and solving. All techniques are standard with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Sketch the graph of $y = \sec x$ for $0 \leq x \leq 2\pi$. [2]
\item Solve the equation $\sec x = 3$ for $0 \leq x \leq 2\pi$, giving the roots correct to 3 significant figures. [3]
\item Solve the equation $\sec \theta = 5 \cos \theta$ for $0 \leq \theta \leq 2\pi$, giving the roots correct to 3 significant figures. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q7 [9]}}