Question

What is $\dfrac{\pi }{10}$ radians in degrees?

Answer 1

The measurement of angles can be done in two different units namely radian and degree. In geometry, we measure the angles in degree but also in radians sometimes, similarly in trigonometry, we measure the angle in radians but sometimes in degrees too. So, there are different kinds of units for determining the angle that are, degrees and radians. There is a simple formula to convert one form of representation to another that is $1radian=\dfrac{180}{\pi }\text{degrees}$ . Using that formula, we can find out the correct answer.

Complete step-by-step solution:
We know that the value of a $\pi$ radians is equal to 180 degrees.
So, the value of 1 radian is equal to
$\Rightarrow 1radian=\dfrac{180}{\pi }\text{degrees}$
So, the value of X radians is equal to
$\Rightarrow Xradian=\dfrac{180}{\pi }\text{degrees}\times \text{X}$
This is the general formula to convert any angle in radians to degrees Thus, the value of $\dfrac{\pi }{10}$ radians is equal to
$\Rightarrow \dfrac{\pi }{10}radian=\dfrac{180}{\pi }\text{degrees}\times \dfrac{\pi }{10}$
$\Rightarrow \dfrac{\pi }{10}radian=18\text{degrees}$
Hence $\dfrac{\pi }{10}$ radians is equal to 18 degrees or ${{18}^{\circ }}$.

Note: A half-circle makes an angle equal to 180 degrees or we can say $\pi$ radians. So, to find out the value of radian, we simply divide 180 degrees by $\pi$ The approximate value of 1 radian is equal to 57.2958 degrees. Now, to convert a given number of radians into degrees we multiply the radians by $\dfrac{180}{\pi }$ and then we have to simply carry out the multiplication. This is a very simple formula and can be used to solve similar questions.