| Exam Board | CAIE |
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| Module | P2 (Pure Mathematics 2) |
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| Year | 2004 |
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| Session | June |
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| Topic | Harmonic Form |
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4
- Express \(3 \sin \theta + 4 \cos \theta\) in the form \(R \sin ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), giving the value of \(\alpha\) correct to 2 decimal places.
- Hence solve the equation
$$3 \sin \theta + 4 \cos \theta = 4.5$$
giving all solutions in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\), correct to 1 decimal place.
- Write down the least value of \(3 \sin \theta + 4 \cos \theta + 7\) as \(\theta\) varies.