Question

How do you convert $-\dfrac{12\pi }{5}$ radian into degree?

Answer 1

We have given numbers as $-\dfrac{12\pi }{5}$ radian, we have to convert it into degrees. To do so we will learn about the relation between the degree and radian, we will use the relation ${{180}^{\circ }}=\pi$Radian, we say $\pi$radian $={{180}^{\circ }}$ degree. To solve our problem we will also use the unitary method to find the value of the given value.

Complete step-by-step solution:
We are $-\dfrac{12\pi }{5}$ radian and we are asked to convert it to degree.
Before we start solving, we will learn that dimensional analysis is a method which helps us in converting the form from one dimension to another dimension which actually changes the value of quantity.
For example we know that 1 meter is the same as 100 cm, here quality is same but dimensional are different.
So we will use dimensional analysis.
We will look at the relation between degree and the radian.
We get
180 degree$=\pi$ radian
Or
We may units this as
$\pi$ Radian = 180 degree
Now, we will use a unitary method to find the value of 1 degree or 1 radian and then use it further.
Now as
$\pi$ Radian ${{180}^{\circ }}$
So by unitary method
1 Radian $=\dfrac{180}{\pi }$
We are given that we have to convert
$\dfrac{-12\pi }{5}$ Radian to degree
Since one radian is $\dfrac{180}{\pi }$
So to find $\dfrac{-12\pi }{5}$radian, we multiply it with $\dfrac{180}{\pi }$
So
$\dfrac{-12\pi }{5}$Radian =$\dfrac{180}{\pi }\times \dfrac{-12\pi }{5}$degree
Simplifying, we get
$=432$
So we get
$\dfrac{-12\pi }{5}$Radian is the same as -432 degrees.

Note: We need not to change $\pi$ into $\dfrac{22}{7}$ form, as mostly it will get convert into process also we can wait always till the last moment we do not direct start multiplying term in numerator or denominator became, it will get long while we stay put and cancel as much as possible in numerator and denominator. Also remember unitary methods always help to find the value of an item if we know the value of the term.