| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2002 |
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| Session | November |
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| Topic | Harmonic Form |
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5
- Express \(4 \sin \theta - 3 \cos \theta\) in the form \(R \sin ( \theta - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), stating the value of \(\alpha\) correct to 2 decimal places.
Hence
- solve the equation
$$4 \sin \theta - 3 \cos \theta = 2$$
giving all values of \(\theta\) such that \(0 ^ { \circ } < \theta < 360 ^ { \circ }\),
- write down the greatest value of \(\frac { 1 } { 4 \sin \theta - 3 \cos \theta + 6 }\).