| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Convert to quadratic in sin/cos |
| Difficulty | Standard +0.3 This is a standard trigonometric equation requiring routine algebraic manipulation using identities (cosec = 1/sin, cos 2θ = 1 - 2sin²θ) to convert to quadratic form, then solving a straightforward quadratic equation. The techniques are well-practiced in C3, though the multi-step nature and need to recall multiple identities makes it slightly above average difficulty. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Express the equation $\cosec \theta(3 \cos 2\theta + 7) + 11 = 0$ in the form $a \sin^2 \theta + b \sin \theta + c = 0$, where $a$, $b$ and $c$ are constants. [3]
\item Hence solve, for $-180° < \theta < 180°$, the equation $\cosec \theta(3 \cos 2\theta + 7) + 11 = 0$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2010 Q3 [6]}}