Question

What is the radian value of $60{}^\circ 30'$?
$\begin{align}
  & \left( A \right)\dfrac{{{\pi }^{c}}}{3} \\
 & \left( B \right)\dfrac{121{{\pi }^{c}}}{360} \\
 & \left( C \right)\dfrac{121{{\pi }^{c}}}{180} \\
 & \left( D \right)\dfrac{121{{\pi }^{c}}}{540} \\
\end{align}$

Answer 1

Hint: In this question, we are given a value in degrees and minutes. Firstly, we will convert it only into degrees to simplifying our answer. After that, we will use the formula of converting $180{}^\circ $ to radians and use it to find radian values of $60{}^\circ 30'$ using the unitary method also. Formula for changing degrees to radian is given as $180{}^\circ ={{\pi }^{c}}$.

Complete step by step answer:
Here, we are given a value $60{}^\circ 30'$ which is in degrees and minutes. We have to find its value in radians. For this, let us first change minutes into degrees.
As we know, sixty minutes make one degree. Therefore, $60'=1{}^\circ $.
We are given $30'$, therefore $30{}^\circ =\dfrac{1}{2}'$.
Value given is $60{}^\circ 30'$. Hence, value purely in degrees becomes $60{}^\circ +\dfrac{1}{2}{}^\circ $.
Taking LCM, we get $\dfrac{121}{2}{}^\circ $. Hence, we have converted $60{}^\circ 30'$ into degrees only to easily find our answer.
Now we will use the formula for converting degrees to radians to convert $\dfrac{121}{2}{}^\circ $.
Formula for converting degrees to radians is given by –
$180{}^\circ ={{\pi }^{c}}$
Using unitary method,
$1{}^\circ ={{\left( \dfrac{\pi }{180} \right)}^{c}}$
For $\left( \dfrac{121}{2} \right){}^\circ $, we get ${{\left( \dfrac{121}{2}\times \dfrac{\pi }{180} \right)}^{c}}$
Solving the above answer, we get ${{\left( \dfrac{121\pi }{360} \right)}^{c}}$
Hence, we have converted $60{}^\circ 30'$ into radians which gives us answer as ${{\left( \dfrac{121\pi }{360} \right)}^{c}}$

So, the correct answer is “Option B”.

Note: Students should know that $180{}^\circ ={{\pi }^{c}}$ and not $1{}^\circ ={{\pi }^{c}}$. They should always learn these formulas for solving faster and easily. They should take care while converting minutes into degrees. Don’t forget that $60$ minutes combine to become $1{}^\circ $. After converting minutes into degrees, they should be added to the given degrees. In degree, $\pi $ gives us the value as $180{}^\circ $ whereas in radian, it gives us the value as $\dfrac{22}{7}$.