Question

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

Answer 1

Hint: Here, the question is to convert the given radian in degrees. Conversion of degrees to radian and radians to degrees are very simple to the extent of the given formulas. By using the formula we will be able to find the correct answer faster.

Formula used:
For converting from degrees to radians we use,
angle in degrees\[ \times \dfrac{\pi }{{180}}\]
For converting from radians to degrees,
\[{\text{angle in radians}} \times \dfrac{{180}}{\pi }\]

Complete Step by Step Solution:
In this question, we are asked to convert $\dfrac{{7\pi }}{3}$ radian to degrees. We will do this by using the above mentioned formula.
For any value of angles, let the angle be $x$ degrees
then, converting from degrees to radians we will use,
\[x \times \dfrac{\pi }{{180}}\]
If we need to convert from radians to degrees, let the angle be $y$ in radians then
\[y \times \dfrac{{180}}{\pi }\]
Now, since we have to convert $\dfrac{{7\pi }}{3}$ radian to degrees we will use the second one
That is for converting from radian to degrees we will use, \[y \times \dfrac{{180}}{\pi }\]
So here $y = \dfrac{{7\pi }}{3}$
Substituting $y = \dfrac{{7\pi }}{3}$ in the formula \[y \times \dfrac{{180}}{\pi }\]
\[\dfrac{{7\pi }}{3} \times \dfrac{{180}}{\pi }\]
Pi and pi will get cancelled, it becomes
\[ = \dfrac{7}{3} \times 180\]
We just multiply the numerator and we get,
\[ = \dfrac{{1260}}{3}\]
Dividing it, we get
$ = 420$

Therefore the degree value of $\dfrac{{7\pi }}{3}$ is $420^\circ $.

Note: Alternative method:
One way to remember these formulas is to think of this way:
If we want to find something in radians and the value is given in the degrees,
As we know, $180^\circ $ is or can be represented as $\pi $ ,
$\pi = 180$ degrees
And we need to convert the given value in degrees which is $y$ ,
$\dfrac{{7\pi }}{3}$ radians = $y$
We can simply cross multiply both the ones,
That is
\[ \Rightarrow \pi = 180\]
$ \Rightarrow \dfrac{{7\pi }}{3} = y $
Cross multiplying,
$\pi y = 180 \times \dfrac{{7\pi }}{3}$
Pi and pi will get cancelled here,
$ \Rightarrow y = \dfrac{{1260}}{3}$
$ \Rightarrow y = 420$
Therefore the degree value of $\dfrac{{7\pi }}{3}$ is $420^\circ $