\chapter{Analytic trigonometry}

    \section{Sum/difference and double angle identities}
    
    


 Check your understanding 




Answer the questions.
\begin{enumerate}
\item Answer True or False:


    

  1. 
\(\sin(30^\circ +\theta)=0.5+\sin \theta\), because \(\sin(30^\circ)=0.5\)
    2. 


  2. 
If \(\cos(x-y)=0\), then we must have \(\cos x=\cos y\)
    3. 


  3. 
If \(\sin \theta = 0.3\), then \(\sin(2\theta)=0.6\)
    4. 



\item
What is the sum/difference identity for \(\cos(x+y)\)?

\item
What is the double angle identity for \(\sin(2x)\)?

\item
State at least one double angle identity for \(\cos(2x)\)

\item
How should we split the angles to use sum/difference identities?
\[
\begin{array}{ccc}
\mbox{i. } 165^\circ & \mbox{ii. } 285^\circ & \mbox{iii. } 195^\circ
\end{array}
\]

\item
How should we split the fractions to use sum/difference identities?

\[
\begin{array}{ccc}
\mbox{i. } \displaystyle \frac{\pi}{12} & \mbox{ii. } \displaystyle \frac{5\pi}{12} & 
\mbox{iii. }\displaystyle \frac{11\pi}{12}
\end{array}
\]

\item
Answer True or False:


    

  1. 
If we know \(\sin x\), then we can find \(\sin(2x)\)
    2. 


  2. 
If we know \(\cos x\), then we can find \(\cos(2x)\)
    3. 


  3. 
If we know both \(\sin x\) and \(\cos x\), then we can find \(\sin(2x)\)
    4. 


  4. 
If we know \(\sin x\), then we can find \(\cos(2x)\)
    5. 


\end{enumerate}






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