| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Equation with non-equation preliminary part (sketch/proof/identity) |
| Difficulty | Standard +0.3 Part (i) is a straightforward application of the Pythagorean identity requiring algebraic manipulation with surds. Part (ii) involves solving a trigonometric equation with a multiple angle, requiring knowledge of the cosine graph and careful consideration of the range—standard C2 material but with multiple solutions to find. Both parts are routine exercises slightly above average difficulty due to the surd manipulation and multiple angle work. |
| 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 Given that $\sin \theta = 2 - \sqrt{2}$, find the value of $\cos^2 \theta$ in the form $a + b\sqrt{2}$ where $a$ and $b$ are integers. [3]
\item Find, in terms of $\pi$, all values of $x$ in the interval $0 \leq x < \pi$ for which
$$\cos 3x = \frac{\sqrt{3}}{2}.$$ [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q5 [8]}}