| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Given one function find others |
| Difficulty | Moderate -0.3 This is a straightforward trigonometric question requiring standard techniques: using Pythagoras to find cos θ from sin θ, then applying the definitions of cot θ and the double angle formula for cos 2θ. While it requires multiple steps and exact value manipulation, these are routine C3 skills with no problem-solving insight needed, making it slightly easier than average. |
| 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 formulae |
It is given that $\theta$ is the acute angle such that $\sin \theta = \frac{12}{13}$. Find the exact value of
\begin{enumerate}[label=(\roman*)]
\item $\cot \theta$, [2]
\item $\cos 2\theta$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q2 [5]}}