ACJC Tutorial 7 Q9

The functions \(\mathrm{f}(\theta )\) and \(\mathrm{g}(\theta )\) are defined such that

\(\mathrm{f}(\theta )=\cos \theta +\sqrt{9-{{\sin }^{2}}\theta }\), \(\mathrm{g}(\theta )=4-\frac{2}{3}{{\theta }^{2}}\).

Find the range of values of \(\theta \) such that \(\mathrm{f}(\theta )\) and \(\mathrm{g}(\theta )\) differ by at most \(0.1\).