An R-formula equation with endpoint solutions

An R-formula equation with endpoint solutions

Secondary 4
6 marks
TGM Original Questions

Consider \(9\cos x+12\sin x\), with \(x\) in degrees.

  1. Express the expression as \(R\cos(x-\alpha)\), where \(R>0\) and \(0^\circ<\alpha<90^\circ\).[3]
  2. Hence solve \(9\cos x+12\sin x=9\) for \(0^\circ\le x\le360^\circ\). Give non-exact angles to 1 decimal place.[3]

Solution:

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Answer:(a) \(15\cos(x-\alpha)\), \(\alpha=\tan^{-1}(4/3)\). (b) \(0^\circ,106.3^\circ,360^\circ\).

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