(a)
The graph of \(y = \cos x\) for \(0^{\circ} \leq x \leq 360^{\circ}\) is a wave starting at \((0^{\circ}, 1)\), decreasing to \((180^{\circ}, -1)\), and returning to \((360^{\circ}, 1)\). Key points: peaks at \(0^{\circ}\) and \(360^{\circ}\), trough at \(180^{\circ}\), and zeros at \(90^{\circ}\) and \(270^{\circ}\).
(b) Ans: 75.5° and 284.5°
Rearrange the equation: \(4\cos x + 2 = 3 \implies \cos x = \frac{1}{4}\).
Find the principal solution: \(x = \cos^{-1}(0.25) \approx 75.52^{\circ}\).
Using the symmetry of the cosine function, the second solution is \(x = 360^{\circ} – 75.52^{\circ} \approx 284.48^{\circ}\).
