| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Solve equation using Pythagorean identities |
| Difficulty | Moderate -0.3 This question requires knowledge of the standard trigonometric identity cosec²θ = 1 + cot²θ, followed by solving a straightforward quadratic equation in cot θ and finding angles. It's a routine multi-step problem testing identity manipulation and equation solving, slightly easier than average due to the direct substitution and standard quadratic factorization involved. |
| Spec | 1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
Given that $\cosec^2 \theta - \cot \theta = 3$, show that $\cot^2 \theta - \cot \theta - 2 = 0$.
Hence solve the equation $\cosec^2 \theta - \cot \theta = 3$ for $0° \leqslant \theta \leqslant 180°$. [6]
\hfill \mbox{\textit{OCR MEI C4 Q1 [6]}}