Question

How do you convert \[\dfrac{5\pi }{12}\] into degrees ?

Answer 1

Hint: The construction between two straight rays drawn from the same fixed vertex is called an angle. As we have many units to denote the measurement of length, in the same manner, angle has more than one unit which we can use according to our convenience. Radians and degrees both are the units of angles that are used accordingly.
But we can change radians into degrees and vice versa. And there is a specific relation between both of these.This relation is-
\[\dfrac{Angle\text{ }in\text{ }degrees}{angle\text{ }in\text{ }radians}\text{ }=\dfrac{180{}^\circ }{\pi }\]

Complete Step by Step Solution:
In this particular question, we are given the value of the angle in radians and we have to change it into degrees.
The relation between angle in radians and degrees is given by :
\[\dfrac{Angle\text{ }in\text{ }degrees}{angle\text{ }in\text{ }radians}\text{ }=\dfrac{180{}^\circ }{\pi }\].
 We can use the above relation to finding the value of the angle in degrees.
Therefore , \[angle\text{ }in\text{ }degrees=\dfrac{180{}^\circ \times angle\text{ }in\text{ }radians}{\pi }\]
\[=\dfrac{\left( 180{}^\circ \times \dfrac{5\pi }{12} \right)}{\pi }\]
\[=15\times 5\]. (π gets cancelled and $12$ and $180$ get divided by $12$ )

So , the value of \[\dfrac{5\pi }{12}\] in degrees is \[75{}^\circ \].

Note:
$1$ radian is defined as the length of the arc of the circle which is equal to the radius of the circle and is subtended by the given angle. We can also use the above relation to find the value of the angle in radians if we are given the angle in degrees. $1$ degree, however, is defined as the measure of \[1/360th\] of the complete revolution of the angle's magnitude.