| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Rational trig expressions |
| Difficulty | Moderate -0.3 This is a straightforward trigonometric equation requiring basic identity manipulation (tan θ = sin θ/cos θ) to reach a quadratic in sin θ, then solving for standard angles. The algebraic rearrangement is guided by part (i), and the solutions are common angles (30° and 90°). Slightly easier than average due to the scaffolding and routine nature of the techniques. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Show that the equation $\frac{\tan \theta}{\cos \theta} = 1$ may be rewritten as $\sin \theta = 1 - \sin^2 \theta$. [2]
\item Hence solve the equation $\frac{\tan \theta}{\cos \theta} = 1$ for $0° \leq \theta \leq 360°$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q9 [5]}}