Question

How do you convert $\dfrac{{3\pi }}{5}$ into degrees?

Answer 1

Here we have to convert $\dfrac{{3\pi }}{5}$ into degree measure. To convert radian into degree measure we will use the formula $\deg = \dfrac{{180}}{\pi } \times rad$. Degree is defined as the measurement of a plane angle in which one full rotation is equal to $360^\circ$. It is denoted by the symbol $(^\circ )$.

Complete step by step answer:
In this problem we have to convert radian measure into degree measure. A radian measure is defined as the angle subtended by an arc of length equal to the radius of the circle at its centre. A radian is a unit of angle measurement.
Degree measure is defined as if the rotation from the initial side to the terminal side is $\dfrac{1}{{360}}$th of one revolution, then the angle is said to have a measure of one degree and is written as $1^\circ$. A degree is further divided into $60$ equal parts and each part is called one minute, denoted as $1'$ and each minute is further divided into $60$ equal parts and each part is called as one second and denoted as .
Now, we will convert $\dfrac{{3\pi }}{5}$ into degrees.
We know that $\deg = \dfrac{{180}}{\pi } \times rad$
So, $\deg = \dfrac{{180}}{\pi } \times \dfrac{{3\pi }}{5}$
$\Rightarrow \deg = \dfrac{{180 \times 3}}{5}$
$\Rightarrow \deg = \dfrac{{540}}{5}$
$\Rightarrow \deg = 108^\circ$
Hence, $\dfrac{{3\pi }}{5}$ is equal to $108^\circ$.

Note:
It is to be noted that the radian measure does not depend upon the radius of the circle. A radian is a measure of an angle and measure of an angle is a real number. The angle which intercepts an arc of length of one unit of a circle is called one radian. The system of measuring angle in radians is more accurate and useful because it tells exactly the arc length that is subtending the angles. The arc that subtends the angle of full rotation is the entire circumference of the circle thus formed.