Answer:
[tex]cos(\alpha-\beta)=-0.9691[/tex]
Explanation: The diagram of the alpha and the beta angles is as follows:
the angles are as follows:
[tex]\begin{gathered} \arctan (-\frac{12}{5})=-67.38^{\circ}\Rightarrow\alpha=180+(-67.38^{\circ})=112.62^{\circ} \\ \alpha=112.62^{\circ} \\ \arccos (\frac{3}{5})\Rightarrow arc\cos (0.6)=53.1^{\circ} \\ \beta=360^{\circ}-53.1^{\circ}=306.9^{\circ} \\ \beta=306.9^{\circ} \\ \therefore\Rightarrow \\ cos(\alpha-\beta)=\cos (112.62^{\circ}-306.9^{\circ}) \\ \cos (-194.28^{\circ})=-0.9691 \end{gathered}[/tex]
Therefore the answer is:
[tex]cos(\alpha-\beta)=-0.9691[/tex]
