OCR C3 — Question 7 9 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSketch reciprocal function graphs
DifficultyModerate -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.
Spec1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals

  1. Sketch the graph of \(y = \sec x\) for \(0 \leq x \leq 2\pi\). [2]
  2. Solve the equation \(\sec x = 3\) for \(0 \leq x \leq 2\pi\), giving the roots correct to 3 significant figures. [3]
  3. Solve the equation \(\sec \theta = 5 \cos \theta\) for \(0 \leq \theta \leq 2\pi\), giving the roots correct to 3 significant figures. [4]

\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]}}