Q1 Find the radian measures corresponding to the following degree measures:

(i) 25 \degree
(ii)-47 \degree30'
(iii) 240\degree
(iv)520\degree

Answers (1)

Solution 

It is solved using relation between degree and radian

(i) 25\degree
We know that  180\degree = \pi radian 

So,      1\degree = \frac{\pi }{180}      radian


 25\degree = \frac{\pi }{180}\times 25   radian    =\frac{5\pi }{36}   radian      
(ii)   -47\degree30'
 We know that
          -47\degree30' = -47\frac{1}{2}degree = -\frac{95}{2}\degree

Now, we know that       180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180}   radian
   
So,    -\frac{95}{2}\degree = \frac{\pi}{180}\times \left (-\frac{95}{2} \right ) radian  \Rightarrow \frac{-19\pi}{72}  radian        
(iii)   240\degree
We know that 
        
      180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180}   radian

So, 240\degree = \frac{\pi}{180}\times 240 \Rightarrow \frac{4\pi}{3}   radian      
(iv)   520\degree
 We know that 

               180\degree = \pi \Rightarrow 1\degree = \frac{\pi}{180}   radian

So, 520\degree \Rightarrow \frac{\pi}{180}\times 520  radian \Rightarrow \frac{26\pi}{9} radian      

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