R-formula and maximum value

R-formula and maximum value

Secondary 4
TGM Original Questions

Express \(5\sin x+12\cos x\) as \(R\sin(x+\alpha)\), where \(0^\circ<\alpha<90^\circ\), and find its maximum value.

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Answer:\(13\sin(x+\alpha)\), where \(\alpha=\tan^{-1}\!\left(\dfrac{12}{5}\right)\approx67.4^\circ\); maximum \(13\).

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