Question

How do you convert $\dfrac{4\pi }{5}$ radians to degree?

Answer 1

Hint: In this question we have to convert the given value of radians into degree. For conversion we will use the following formula of conversion $\text{Degree=radian}\times \dfrac{180{}^\circ }{\pi }$.

Complete step by step answer:
We have been given $\dfrac{4\pi }{5}$ radians.
We have to convert it into degrees.
We know that degrees and radians are two different units of the measurement of angles in geometry. The measurement of an angle is determined by the amount of rotation that takes place from initial side to terminal side. An angle can be determined by either radian or degree.
To convert radians into degree we just need to multiply the given radians by $\dfrac{180{}^\circ }{\pi }$ and need to simplify the expression.
We have given $\dfrac{4\pi }{5}$ radians. By using the conversion formula we will get
$\text{Degree=}\dfrac{4\pi }{5}\times \dfrac{180{}^\circ }{\pi }$
Now, simplifying the above expression we will get
$\begin{align}
  & \Rightarrow \dfrac{4\times 180{}^\circ }{5} \\
 & \Rightarrow 144{}^\circ \\
\end{align}$
Hence we get the required value of $\dfrac{4\pi }{5}$ radians as\[144{}^\circ \].

Note: A degree has also sub parts as minutes and seconds. To define a radian we have to use the central angle. We have other conversion formulas as $1{}^\circ =60'$ and $1'=60''$ where ‘ refers to minutes and “ refers to seconds. We can also use the value of $\pi $ as $3.14$ in the formula to simplify the obtained equation if $\pi $ is not given in the question. We can use the same formula which is given as $\text{Degree=radian}\times \dfrac{180{}^\circ }{\pi }$ to convert the degrees into radians.