| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Multiple angle equations |
| Difficulty | Moderate -0.3 This question tests routine manipulation of reciprocal trig functions and standard solving techniques. Part (a) requires converting sec to cos and handling the half-angle (straightforward substitution), while part (b) uses the identity tan·cot=1 to reach tan²β=7. Both are standard textbook exercises with clear methods and no novel problem-solving required, making them slightly easier than average A-level questions. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
3
\begin{enumerate}[label=(\alph*)]
\item Solve, for $0 ^ { \circ } < \alpha < 180 ^ { \circ }$, the equation $\sec \frac { 1 } { 2 } \alpha = 4$.
\item Solve, for $0 ^ { \circ } < \beta < 180 ^ { \circ }$, the equation $\tan \beta = 7 \cot \beta$.
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2008 Q3 [7]}}