Question

How do you convert $\dfrac{\pi }{{12}}$ to degrees?

Answer 1

Hint : Angles are the measure of rotation between two lines. Radian and degree are the two different units used for the measurement of the angles. We measure the angles in degree in geometry but also in radians sometimes, similarly in trigonometry, we measure the angle in radians but sometimes in degrees too. To convert one form of representation to another, we use a simple formula. In this question, we are given the angle in radians and we have to convert it into radians so using that formula, we can find out the correct answer.

Complete step-by-step answer :
We know that the value of $\pi$ radians is equal to 180 degrees.
So the value of 1 radian is equal to $\dfrac{{180}}{\pi }$ degrees.
The value of x radians is equal to $x \times \dfrac{{180}}{\pi }$ degrees.
This is the general formula to convert any angle in radians to degrees.
Thus the value of $\dfrac{\pi }{{12}}$ radians is equal to $\dfrac{\pi }{{12}} \times \dfrac{{180}}{\pi } = \dfrac{{180}}{{12}}$ degrees.
Now, we simplify this fraction –
$\dfrac{{180}}{{12}} = \dfrac{{2 \times 2 \times 3 \times 3 \times 5}}{{2 \times 2 \times 3}} = 15^\circ$
Hence, $\dfrac{\pi }{{12}}$ radians is equal to 15 degrees
So, the correct answer is “ $15^\circ$ ”.

Note : We multiply the radians by $\dfrac{{180}}{\pi }$ to convert a given amount of radians into degrees and then we have to simply carry out the multiplication. This is a very simple formula and can be used to solve similar questions. For simplifying the fraction obtained, we write both the numerator and the denominator as the product of its prime factors and then cancel out the common factors. Following similar steps, we can also derive a formula for converting degrees into radians.