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  • Find the degree measures corresponding to the following radian measures (use pi = 22\7)

Q(2) Find the degree measures corresponding to the following radian measures.  (Use \small \pi =\frac{22}{7})

 \small (i) \frac{11}{16}
\small (ii) -4
\small (iii) \frac{5\pi }{3}
\small (iv) \frac{7\pi }{6}

Answers (1)

Solution 

(1)   \frac{11}{16}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree

So,   \frac{11}{16} radian = \frac{180}{\pi}\times \frac{11}{16}degree                            (we need to take \pi = \frac{22}{7} )

   \frac{11}{16}radian = \frac{180\times 7}{22}\times \frac{11}{16}degree \Rightarrow \frac{315}{8}degree 
 
                                                                                             (we use 1\degree = 60' and 1' = 60'')

Here 1' represents 1 minute and 60" represents 60 seconds
Now, 

\frac{315}{8}degree=39\frac{3}{8}degree\\ \\ =39\degree +\frac{3\times 60}{8}minutes \Rightarrow 39\degree +22' + \frac{1}{2}minutes \Rightarrow 39\degree +22' +30''\\ \\ \Rightarrow \frac{315}{8}degree = 39\degree22'30''                                                                                                             

(ii)  -4
We know that

\pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree             (we need to take \pi = \frac{22}{7} )


So,  -4 radian =  \frac{-4\times 180}{\pi} \Rightarrow \frac{-4\times 180\times 7}{22} \Rightarrow \frac{-2520}{11}degree                                                                                                                   


                                                                                            (we use 1\degree = 60' and 1' = 60'')

\Rightarrow \frac{-2520}{11}degree = -229\frac{1}{11}degree =-229\degree + \frac{1\times 60}{11}minutes \\ \\ \Rightarrow -229\degree + 5' + \frac{5}{11}minutes = -229\degree +5' +27''\\ \\ -\frac{2520}{11} = -229\degree5'27''


(iii)   \frac{5\pi}{3}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree    (we need to take \pi = \frac{22}{7} )


So,  \frac{5\pi}{3}radian = \frac{180}{\pi}\times \frac{5\pi}{3}degree = 300\degree       
(iv)  \frac{7\pi}{6}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree        (we need to take \pi = \frac{22}{7} )


So, \frac{7\pi}{6}radian = \frac{180}{\pi}\times \frac{7\pi}{6} = 210\degree           

Posted by

Safeer PP

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