| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Show equation reduces to tan form |
| Difficulty | Moderate -0.8 This is a straightforward application of the addition formula for sine, followed by basic algebraic manipulation to isolate tan θ. Part (i) requires expanding sin(θ+45°) using the given exact values and rearranging to get tan θ = (√2-1), which is routine. Part (ii) involves using a calculator to find angles from the tan value. The question tests standard technique with no problem-solving insight required, making it easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks |
|---|---|
| \(= 2 - \phi = 2 - \left(\frac{1 + \sqrt{5}}{2}\right)\) | M1 A1 |
| \(= \frac{3 - \sqrt{5}}{2}\) | A1 |
$1 - EH = 1 - CG = 1 - (\phi - 1)$
$= 2 - \phi = 2 - \left(\frac{1 + \sqrt{5}}{2}\right)$ | M1 A1 |
$= \frac{3 - \sqrt{5}}{2}$ | A1 |4 The angle $\theta$ satisfies the equation $\sin \left( \theta + 45 ^ { \circ } \right) = \cos \theta$.\\
(i) Using the exact values of $\sin 45 ^ { \circ }$ and $\cos 45 ^ { \circ }$, show that $\tan \theta = \sqrt { 2 } - 1$.\\
(ii) Find the values of $\theta$ for $0 ^ { \circ } < \theta < 360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C4 2008 Q4 [7]}}