Question

How do you convert $\dfrac{7\pi}{3}$ to degrees?

Answer 1

Hint: Given an angle in Pie Radian form and we have to convert it into degrees. For this we will use the conversion:
$\pi\ radian = 180^\circ$
I radian =180
So we will multiply by 180.
 To convert Radian to degree by solving the expression will find the value

Complete step-by-step answer:
Step1: We are given an angle in radian i.e.$\dfrac{{7\pi }}{3}$ in order to convert radians to degrees, multiply by 180, since a full circle is $360^\circ$ or 2π radian .
$ \Rightarrow \left( {\dfrac{{7\pi }}{3}} \right).\dfrac{{180}}{\pi }$
Now we will factor out $\pi $ of $7\pi $ we will get:
$ \Rightarrow \dfrac{{\pi .7}}{3} \times \dfrac{{180}}{\pi }$
Cancel the common factor i.e.$\pi $ and rewrite the expression:
$ \Rightarrow \dfrac{7}{3} \times 180$
Step2: Now we will factor out common factor $3$ we will get:
$ \Rightarrow \dfrac{7}{3} \times \left( {3\left( {60} \right)} \right)$
Cancel the common factor and rewrite the expression:
$ \Rightarrow 7 \times 60$
After multiplication we will get:
$ \Rightarrow {420^0}$

Step3: Final answer: Hence the answer is ${420^0}$

Additional information:
Pi doesn't equal any number of degrees because pi without a unit is just a number. The Point is that pi Radians are equal to 180 degrees. Radians are a unit of measurement for angles, just like degrees are and pi is just like the number of radians that makes up that angle.

Note:
In such types of questions of conversion students should know the conversion ratio. They should remember what should be multiplied or divided to convert from one form to another. To convert from degree to Radian we will divide the value in degrees by 180/π. Calculation is easy but keep in mind while writing the value of π. Because it has two values 3.14 or 22/7. Use the one value from starting both are right but for one solution use one value so that there should not be any error in the answer.