Question

Convert the angle $\dfrac{\pi }{6}$ from radians into degrees.

Answer 1

Hint: There are many units for measuring an angle. Two of these units are radians and degrees. It is possible to convert an angle from one unit to another unit. To convert an angle that is measured in radians to degrees, we must know that $\pi$ in radians is equal to 180 in degrees. Using this information, we can solve this question.

Complete step by step solution:
Before proceeding with the question, we must know the formula that will be required to solve this question.
To convert an angle from one unit to another, we have to do some changes in the angle. To convert the angle in radians to angle in degrees, we must know that $\pi$ in radians is equal to 180 in degrees. So, substituting $\pi =180$ in the angle in radians, we can convert it into degrees.
In the question, we are given an angle $\dfrac{\pi }{6}$ in radians and we are required to convert this angle to degrees. From the above paragraph, if we substitute $\pi =180$, we can convert this angle to degrees. Substituting, we get,
$\begin{aligned} & \dfrac{\pi }{6}={{\dfrac{180}{6}}^{\circ }} \\\ & \Rightarrow \dfrac{\pi }{6}={{30}^{\circ }} \\\ \end{aligned}$
Hence, the angle $\dfrac{\pi }{6}$ in radians is equal to ${{30}^{\circ }}$ in degrees.

Note: This is an easy question if one has the basic knowledge to convert an angle from one unit to another unit. One must know that to convert an angle from radians to degrees, we have to substitute $\pi =180$. The only possibility of mistake which can be done in this question is calculation mistake. For example, one may calculate $\dfrac{\pi }{6}={{60}^{\circ }}$ instead of $\dfrac{\pi }{6}={{30}^{\circ }}$.