Convert sums 𝑎 cos(𝑥) + 𝑏 sin(𝑥) to 𝑅 cos(𝑥 ± 𝛼) or 𝑅 sin(𝑥 ± 𝛼) and apply these to sketch graphs.

Consider the function \(f(x) = 5\cos(x) - 12\sin(x)\) where \(x \in \mathbb{R}\). (a) Convert \(f(x)\) into the form \(R\cos(x + \alpha)\), where \(R > 0\) and \(0 < \alpha < \frac{\pi}{2}\). Express \(R\) as an integer and \(\alpha\) in radians correct to 2 decimal places. (3 marks) (b) Hence determine the minimum value of \(f(x)\) and the smallest positive value of \(x\) at which this minimum occurs. Give \(x\) correct to 2 decimal places. (2 marks)

Convert the expression \(f(x) = 5\cos(x) - 12\sin(x)\) to the form \(R\cos(x + \alpha)\), where \(R > 0\) and \(0 < \alpha < 2\pi\).

Convert \(f(x) = 5\cos(x) - 12\sin(x)\) into the form \(R\cos(x + \alpha)\), where \(R > 0\) and \(0 < \alpha < \frac{\pi}{2}\). Express \(\alpha\) in radians correct to two decimal places.