Question

How to convert $\dfrac{{4\pi }}{2}$ radians to degrees ?

Answer 1

To convert the radian measure to degree measure, we first multiply the radian measure by ${\left( {\dfrac{{180}}{\pi }} \right)^ \circ }$so as to get the angle in degree measure. Then to convert degree to minute, we multiply the degrees by $60'$ to get the result in minutes and to convert the minutes to seconds by multiplying $60''$ to the given number which is in minute the resultant number will be in second.

Complete answer:
Radians and degrees are both units used for measuring angles. As you may know, a circle consists of $2\pi$ radians, which is the equivalent of $360$ degree. Both of these values represent going once around a circle. Therefore, $1\pi$ radian represents going around a semi-circle or covering ${180^ \circ }$. This makes $\dfrac{{{{180}^ \circ }}}{\pi }$ the perfect conversion tool for converting radians to degrees.

To convert from radians to degrees, you simply have to multiply the radian value by $\dfrac{{{{180}^ \circ }}}{\pi }$. Next, one degree (°) is equal to $60$ minutes (') and one minute equals to sixty seconds. So, in turn, 1 degree is equal to $3600$ seconds. So, to convert decimal degrees to minutes, we multiply $60$ to the decimal degree number and next to convert decimal minute to seconds we multiply $60$ to the decimal minute.

Here is the question given $\dfrac{{4\pi }}{2}$ radians. Firstly, we convert radian to degree by multiplying the radian measure by $\dfrac{{{{180}^ \circ }}}{\pi }$.
$\dfrac{{4\pi }}{2} \times \dfrac{{{{180}^ \circ }}}{\pi }$
The value of $\pi$ is 3.14.
Cancelling $\pi$ in numerator and denominator, we get,
$\Rightarrow \dfrac{4}{2} \times \dfrac{{{{180}^ \circ }}}{1}$
Cancelling $2$ in both numerator and denominator, we get,
$\Rightarrow 2 \times {180^ \circ }$
$\Rightarrow {360^ \circ }$
Next, we notice that we don’t have ant decimal degrees. So, we don’t need to convert decimal degrees into minutes and subsequently decimal minutes into seconds.

Hence, the degree measure for the given radian measure $\dfrac{{4\pi }}{2}$ is ${360^ \circ }$.

Note: We can change the number from one form to another. We have a specific method to convert the numbers. Here in this question, we have converted the given number which is in radian to the degree and to the minute and to the second. For the conversion, we have followed the unitary method in which we first find the value of one unit and then multiply it by the desired number of units.