Question

Find the radian measure corresponding to the following degree measure:
$ - {47^\circ}30'$
A) $\dfrac{{19\pi }}{{72}}$
B) $ - \dfrac{{9\pi }}{{72}}$
C) $ - \dfrac{{19\pi }}{{72}}$
D) None of these

Answer 1

Hint: According to the question given in the question we have to determine the radian corresponding degree measure for $ - {47^\circ}30'$. So, first of all we have to convert $ - {47^\circ}30'$ whole into degree and for this we have to use the formula as mentioned below:

Formula used: $ \Rightarrow {1^\circ} = 60'...................(A)$
After converting into degree we have to convert the obtained into radians which can be converted with the help of the formula as mentioned below:
$ \Rightarrow x \times \dfrac{\pi }{{{{180}^{^\circ}}}}..................(B)$
Where x can be any degree which can be converted into radians.

Complete step-by-step solution:
Step 1: First of all we have to convert $ - {47^\circ}30'$ whole into degree and for this we have to use the formula (A) as mentioned in the solution hint.
$
   = - {47^\circ} + \dfrac{{30}}{{60}} \\
   = - {47^\circ} + \dfrac{1}{2}
 $
On solving the L.C.M,
$
   = - \dfrac{{{{(94 + 1)}^\circ}}}{2} \\
   = - \dfrac{{{{95}^\circ}}}{2}
 $
Step 2: Now, we have to convert the obtained radians which can be converted with the help of the formula (2) as mentioned in the solution hint. Hence,
$
   = \dfrac{{ - {{95}^\circ}}}{2} \times \dfrac{\pi }{{{{180}^\circ}}} \\
   = - \dfrac{{19}}{{72}}\pi
 $
Hence, with the help of the formula (A) and formula (B) we have determined the required radians which is $ - \dfrac{{19}}{{72}}\pi $.

Therefore option (C) is correct.

Note: To convert the given degree into radians it is necessary that we have to convert the whole in pure form of degree which means we also have to convert minutes and seconds into degrees as well.
We can convert minutes into degree easily as we know that ${1^\circ} = 60'$