\chapter{Trigonometry I}

    \section{Using inverse trig functions}
    
    


 Check your understanding 



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

    

  1. 
 \(\sin^{-1}(\sin x)=x\) for all \(x\).
    2. 


  2. 
\(\sin(\sin^{-1} x) =x\) for all \(x\) in the interval \([-1,1]\).
    3. 


  3. 
\(\cos^{-1}(\cos \theta)=\theta\) for all \(\theta\) in the interval \([0,\pi]\).
    4. 


  4. 
\(\tan(\tan^{-1} x)=x\) for all \(x\).
    5. 


  5. 
\(\tan^{-1}(\tan x) =x\) for all \(x\).
    6. 



\item
Suppose \(x\) is a negative number greater than \(-1\), and \(\theta =\cos^{-1}x \). 
Is \(\sin \theta\) positive
or negative?

\item
Answer True or False:

    

  1. 
\(\sin(\cos^{-1} x)\) cannot be re-written in any way, because \(\cos^{-1}\) is not the
inverse of \(\sin\).
    2. 


  2. 
\(\cos(\tan^{-1}(-4))\) does not exist, because the range of \(\cos \) is \([-1,1]\).
    3. 


  3. 
\(\tan(\cos^{-1}x)\) must be always positive, because the range of \(\cos^{-1}\) is
\([0,\pi]\).
    4. 

\end{enumerate}   


    

     Back to Unit 4.10