| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Multiple angle equations |
| Difficulty | Standard +0.8 This question requires converting a mixed tan²/sec equation to a quadratic in sec (using the identity tan²x = sec²x - 1), solving the quadratic, then finding all solutions for 2θ in [0°, 720°] before halving to get θ. The double angle and multiple solutions across two full rotations elevate this above a standard C3 question, but it follows a recognizable pattern once the identity is applied. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item Giving your answers to 1 decimal place, solve the equation
\end{enumerate}
$$5 \tan ^ { 2 } 2 \theta - 13 \sec 2 \theta = 1 ,$$
for $\theta$ in the interval $0 \leq \theta \leq 360 ^ { \circ }$.\\
\hfill \mbox{\textit{OCR C3 Q2 [7]}}