Question

How do you change $\dfrac{{7\pi }}{9}$ radians to degree measure?

Answer 1

This problem deals with solving or actually converting the given value of radians measure to degree measure. Given the value is in radian measure form. This can be done, that is the conversion from radians measure to degree measure can be done by multiplying the given value of radians with the constant $\dfrac{{180}}{\pi }$. After the multiplication the result is the desired value in degrees.

Complete step-by-step solution:
Given the expression in radians, we have to convert it into degrees, as shown below:
Consider the given expression as shown below:
$\Rightarrow \dfrac{{7\pi }}{9}$
Now to convert it into degrees measure, we have to multiply the given above expression with $\dfrac{{180}}{\pi }$, as shown below:
$\Rightarrow \dfrac{{7\pi }}{9} \times \dfrac{{180}}{\pi }$
Now simplifying the above expression as shown below:
There is a $\pi$ term in the numerator and also a $\pi$ term in the denominator, so it cancels out.
Also on further simplification the 180 term in the numerator is divisible by 9 in the denominator, as shown below:
$\Rightarrow \dfrac{{7\pi }}{9} \times \dfrac{{180}}{\pi } = 7 \times 20$ degrees
$\therefore \dfrac{{7\pi }}{9} \times \dfrac{{180}}{\pi } = 140$degrees.
On conversion of $\dfrac{{7\pi }}{9}$ radians to degrees, the value is equal to ${140^ \circ }$.

Note: Please note that the above problem is solved by converting the given value in radians to degree measure as asked. But when asked to convert the given value of degrees to the radians measure then the conversion is done by multiplying the given value of degree measure with the constant $\dfrac{\pi }{{180}}$, which is also equal to 0.01745 .
So to convert radians to degrees multiply it with $\dfrac{{180}}{\pi }$, where as to convert degrees to radians multiply it with the reciprocal of $\dfrac{{180}}{\pi }$, which is equal to $\dfrac{\pi }{{180}}$ .