| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Solve equation with reciprocal functions |
| Difficulty | Standard +0.3 This question requires knowledge of the Pythagorean identity cot²x + 1 = cosec²x to substitute and form a quadratic in cosec x, then solve and find angles in the given interval. While it involves reciprocal trig functions (C3 content), the solution path is fairly standard once the identity is recognized, requiring routine algebraic manipulation and inverse trig calculations rather than novel insight. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item Find, to 2 decimal places, the solutions of the equation
\end{enumerate}
$$3 \cot ^ { 2 } x - 4 \operatorname { cosec } x + \operatorname { cosec } ^ { 2 } x = 0$$
in the interval $0 \leq x \leq 2 \pi$.\\
\hfill \mbox{\textit{OCR C3 Q2 [6]}}