9. Solve a) \( 2.5 \cos \theta-4.2 \sin \theta=3.6: 0^{\circ} \leq \theta \leq 360 \)\nb) \( 12 \operatorname{Sec} x-1=7 \tan ^{2} x: 0^{\circ} \leq \theta \leq 360^{\circ} \)

To tackle the equation \( 2.5 \cos \theta - 4.2 \sin \theta = 3.6 \), we can rearrange it to isolate \(\theta\). Start by rewriting it as \( 2.5 \cos \theta = 4.2 \sin \theta + 3.6 \) and then express it in terms of tangent or use a substitution like \( R \cos(\theta + \phi) = k \), finding an appropriate \( R \) and \( \phi \) to solve for \(\theta\). This may involve some trigonometric identities and can lead you to possible angles for \(\theta\). For the second part \( 12 \sec x - 1 = 7 \tan^2 x \), remember that \(\sec x = \frac{1}{\cos x}\) and \(\tan^2 x = \frac{\sin^2 x}{\cos^2 x}\). Start by substituting \( \sec^2 x - 1 = \tan^2 x \) to manipulate the equation. Rearranging the equation and solving for specific values leads to solutions within the interval: checking for all angles through substitution and identities ensures complete and accurate calculations. Have fun working through these angle transformations, and remember that practice will solidify your understanding and skills!