| Exam Board | CAIE |
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| Module | P2 (Pure Mathematics 2) |
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| Year | 2015 |
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| Session | November |
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| Topic | Harmonic Form |
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6
- Express \(( \sqrt { } 5 ) \cos \theta - 2 \sin \theta\) in the form \(R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the value of \(\alpha\) correct to 2 decimal places.
- Hence
(a) solve the equation \(( \sqrt { } 5 ) \cos \theta - 2 \sin \theta = 0.9\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\),
(b) state the greatest and least values of
$$10 + ( \sqrt { } 5 ) \cos \theta - 2 \sin \theta$$
as \(\theta\) varies.