| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2009 |
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| Session | November |
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| Topic | Complex numbers 2 |
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7 Use de Moivre's theorem to express \(\sin ^ { 6 } \theta\) in the form
$$a + b \cos 2 \theta + c \cos 4 \theta + d \cos 6 \theta$$
where \(a , b , c , d\) are constants to be found.
Hence evaluate
$$\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \sin ^ { 6 } 2 x d x$$
leaving your answer in terms of \(\pi\).