Question

Find the radian measures corresponding to the following degree measures:

1. ${25}^o$
   
2. $-{47}^{o}30$
   
3. ${240}^o$
   
4. ${520}^o$
   

Answer 1

$1){25}^o$

$Radianmeasure=\frac{\Pi }{180}\ast givenvalue$

$=\frac{\Pi }{180}\ast {25}^o$

$=\Pi \ast \frac{25}{36}$

$=\frac{5\Pi }{36}$

$2)-{47}^o{30}^{{}^{\prime }}$

$=-{(47}^o+{30}^{{}^{\prime }})$

$=-({47}^o+\frac{{30}^o}{60})$

$=-({47}^o+\frac{1^o}{2})$

$=-\left(\frac{{94+1}^o}{2}\right)$

$=-\left(\frac{{95}^o}{2}\right)$

$Radianmeasure=\frac{\Pi }{180}\ast givenvalue$

$=\frac{\Pi }{180}\ast \left(\frac{{95}^o}{2}\right)$

$=\Pi \ast \left(\frac{-19}{72}\right)$

$=\left(\frac{-19\Pi }{72}\right)radians$

$3){240}^o$

$Radianmeasure=\frac{\Pi }{180}\ast givenvalue$

$=\frac{\Pi }{180}\ast {240}^o$

$=\Pi \ast \frac{4}{3}$

$=\frac{4}{3}\Pi radians$

$4){520}^o$

$Radianmeasure=\frac{\Pi }{180}\ast givenvalue$

$=\frac{\Pi }{180}\ast {520}^o$

$=\Pi \ast \frac{26}{9}$

$=\frac{26}{9}\Pi radians$