\chapter{Analytic trigonometry}

    \section{Law of cosines}
    
    


 Check your understanding 




Answer the questions.
\begin{enumerate}
\item 
State the Law of Cosines.

\item
Explain how the difference between the range of the \(\sin^{-1}\) and the \(\cos^{-1}\) functions affects our choice when solving the SAS or SSS cases.

\item
Decide if the following problems can be solved with the Law of cosines, and if they can, determine the case.


    

  1.  \(A\), \(b\), \(c\) given
    2. 


  2.  \(B\), \(C\), \(c\) given
    3. 


  3.  \(A\), \(a\), \(b\) given
    4. 


  4.  \(a\), \(b\), \(c\) given
    5. 


  5.  \(C\), \(a\), \(b\) given
    6. 



\item
Suppose we are solving an SAS case, and we are given angle \(C\), \(a=13\),
\(b=29\). After finding side \(c\) with the law of cosines, which angle should we solve for
using the law of sines?

\item
Suppose we are solving an SSS case, and the three given sides \(a\), \(b\), \(c\) have increasing 
lengths, \(a < b < c\). Which angle should we solve for first?
\end{enumerate}







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