| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Convert sin/cos ratio to tan |
| Difficulty | Moderate -0.8 This is a straightforward C2 question combining routine graph sketching with a standard trigonometric equation. Part (i) requires basic recall of the tan graph shape and asymptotes. Part (ii) is a textbook exercise: divide by cos x to get tan x = 3/4, then use calculator and CAST diagram for second solution. Both parts are simpler than average A-level questions, requiring only standard techniques without problem-solving or insight. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Sketch shown | 2 marks | no numbers required on axes unless more branches shown; G1 for a correct first sweep |
| (ii) \(\tan x = \frac{3}{4}\) | M1 | 5 marks total; 36.8 to 36.9 and 216.8 to 216.9 |
(i) Sketch shown | 2 marks | no numbers required on axes unless more branches shown; G1 for a correct first sweep
(ii) $\tan x = \frac{3}{4}$ | M1 | 5 marks total; 36.8 to 36.9 and 216.8 to 216.9 | A1A1 | Allow 37, 2175 (i) Sketch the graph of $y = \tan x$ for $0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }$.\\
(ii) Solve the equation $4 \sin x = 3 \cos x$ for $0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C2 2006 Q5 [5]}}