| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Multiple independent equations — all direct solve |
| Difficulty | Standard +0.3 This is a standard C3 trigonometric equation question requiring double angle formulas and reciprocal identities. Part (i) uses sin 2θ = 2sin θ cos θ and leads to a quadratic in sin θ. Part (ii) requires recognizing cosec²θ = 1/sin²θ and rearranging. Both are routine applications of A-level identities with straightforward algebraic manipulation, making this slightly easier than average. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
The angle $\theta$ is such that $0° < \theta < 90°$.
\begin{enumerate}[label=(\roman*)]
\item Given that $\theta$ satisfies the equation $6 \sin 2\theta = 5 \cos \theta$, find the exact value of $\sin \theta$. [3]
\item Given instead that $\theta$ satisfies the equation $8 \cos \theta \cosec^2 \theta = 3$, find the exact value of $\cos \theta$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2010 Q2 [8]}}