OCR C3 — Question 3 7 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeMultiple independent equations — all direct solve
DifficultyModerate -0.3 This question tests basic trigonometric equation solving with standard techniques. Part (a) requires converting secant to cosine and solving a simple equation. Part (b) uses the identity tan β = 7 cot β → tan²β = 7, which is straightforward. Both parts involve routine manipulation with no conceptual challenges, making this slightly easier than average for C3.
Spec1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals

  1. Solve, for \(0° < \alpha < 180°\), the equation \(\sec \frac{1}{2}\alpha = 4\). [3]
  2. Solve, for \(0° < \beta < 180°\), the equation \(\tan \beta = 7 \cot \beta\). [4]

\begin{enumerate}[label=(\alph*)]
\item Solve, for $0° < \alpha < 180°$, the equation $\sec \frac{1}{2}\alpha = 4$. [3]
\item Solve, for $0° < \beta < 180°$, the equation $\tan \beta = 7 \cot \beta$. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR C3  Q3 [7]}}