Question

I need help with this practice problem with that is from trigonometry prep book

Answer 1

`cos(\alpha-\beta)=-0.9691`

Step-by-step explanation: The diagram of the alpha and the beta angles is as follows:

the angles are as follows:

`\begin{gathered} \arctan (-(12)/(5))=-67.38^(\circ)\Rightarrow\alpha=180+(-67.38^(\circ))=112.62^(\circ) \\ \alpha=112.62^(\circ) \\ \arccos ((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}`

Therefore the answer is:

`cos(\alpha-\beta)=-0.9691`