| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2010 |
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| Session | November |
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| Topic | Harmonic Form |
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8
- Express \(( \sqrt { } 6 ) \cos \theta + ( \sqrt { } 10 ) \sin \theta\) 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, in each of the following cases, find the smallest positive angle \(\theta\) which satisfies the equation
(a) \(( \sqrt { } 6 ) \cos \theta + ( \sqrt { } 10 ) \sin \theta = - 4\),
(b) \(( \sqrt { } 6 ) \cos \frac { 1 } { 2 } \theta + ( \sqrt { } 10 ) \sin \frac { 1 } { 2 } \theta = 3\).