| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch two trig curves and count intersections/solutions |
| Difficulty | Standard +0.8 This question requires accurate sketching of two non-trivial trigonometric functions (sin 2x with doubled frequency and tan x/2 with halved period including asymptotes), then careful visual analysis to count intersections. While the individual sketches are C2-standard, combining them accurately and identifying all intersection points (including near asymptotes) requires good graphical understanding and is more demanding than routine trig graph questions. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (i) Sketch on the same diagram the graphs of $y = \sin 2 x$ and $y = \tan \frac { x } { 2 }$ for $x$ in the interval $0 \leq x \leq 360 ^ { \circ }$.\\
(ii) Hence state how many solutions exist to the equation
\end{enumerate}
$$\sin 2 x = \tan \frac { x } { 2 } ,$$
for $x$ in the interval $0 \leq x \leq 360 ^ { \circ }$ and give a reason for your answer.\\
\hfill \mbox{\textit{OCR C2 Q1 [6]}}