| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Equation with non-equation preliminary part (sketch/proof/identity) |
| Difficulty | Moderate -0.8 Part (i) is a straightforward trigonometric identity verification using the Pythagorean identity cos²x = 1-sin²x and tan x = sin x/cos x, requiring only direct substitution. Part (ii) is a basic quadratic-type equation in sin y, factoring to sin y(4sin y - 1) = 0, then finding angles in the given range. Both parts are routine C2-level exercises with standard techniques and minimal problem-solving demand. |
| 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, when $x$ is an acute angle, $\tan x \sqrt{1 - \sin^2 x} = \sin x$. [2]
\item Solve $4 \sin^2 y = \sin y$ for $0° \leq y \leq 360°$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2016 Q7 [5]}}