| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Rational trig expressions |
| Difficulty | Standard +0.3 Part (i) requires finding a simple counter-example (e.g., θ = π/2 gives 0, not > 0), which is straightforward. Part (ii) involves algebraic manipulation of the equation to form a quadratic in sin θ, then solving—a standard technique for C3 trigonometric equations. The 7 marks reflect routine application of known methods rather than novel problem-solving. |
| Spec | 1.01c Disproof by counter example1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Prove, by counter-example, that the statement
"$\cosec \theta - \sin \theta > 0$ for all values of $\theta$ in the interval $0 < \theta < \pi$"
is false. [2]
\item Find the values of $\theta$ in the interval $0 < \theta < \pi$ such that
$$\cosec \theta - \sin \theta = 2,$$
giving your answers to 2 decimal places. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [7]}}