| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Integration using De Moivre identities |
| Difficulty | Challenging +1.2 This is a standard Further Maths FP2 question requiring systematic application of de Moivre's theorem to express sin^5θ in terms of multiple angles, then routine integration. While it involves multiple steps and algebraic manipulation, it follows a well-established template that FP2 students practice extensively, making it moderately above average difficulty but not requiring novel insight. |
| Spec | 1.08d Evaluate definite integrals: between limits4.02q De Moivre's theorem: multiple angle formulae |
5. (a) Use de Moivre's theorem to show that
$$\sin ^ { 5 } \theta \equiv a \sin 5 \theta + b \sin 3 \theta + c \sin \theta$$
where $a$, $b$ and $c$ are constants to be found.\\
(b) Hence show that $\int _ { 0 } ^ { \frac { \pi } { 3 } } \sin ^ { 5 } \theta \mathrm {~d} \theta = \frac { 53 } { 480 }$\\
VILM SIHI NITIIIUMI ON OC\\
VILV SIHI NI III HM ION OC\\
VALV SIHI NI JIIIM ION OO
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\hfill \mbox{\textit{Edexcel FP2 2016 Q5 [10]}}