Question

How do you convert $\dfrac{{7\pi }}{6}$ to degrees?

Answer 1

Hint:
This sum is just a part of what the student will have to perform when he/she needs to apply this concept to the chapter of curves or even trigonometric formulae or in the chapter heights and distance. The Student has to multiply by $\dfrac{{180}}{\pi }$ to convert from Radians to Degree. When the question consists of $\pi $ in it, the angle is said to be in radians. If the question is asked to convert from degree to radians the student has to multiply the given angle by $\dfrac{\pi }{{180}}$. If the student gets confused with the conversion, he should remember that radians always have $\pi $in them, so if he has to remove $\pi $, he will have to multiply by a term that has $\pi $ in the denominator. SO by this, he can easily remember that radians to degree conversion are multiplying by $\dfrac{{180}}{\pi }$.

Complete step by step solution:
In the sum, we have to convert the given angle which is in radians to the degree. Since it has $\pi $ in the numerator, if we remove the $\pi $ in the numerator by multiplying it with $\dfrac{{180}}{\pi }$, we will get the angle in degrees.
In order to convert from radians to degrees, we will multiply $\dfrac{{7\pi }}{6}$ by $\dfrac{{180}}{\pi }$
On multiplying $\dfrac{{7\pi }}{6} \times \dfrac{{180}}{\pi }$

$\therefore $Angle in degrees is ${210^ \circ }$.

Note:
Students should memorize this conversion as it is used in many places. This step is used in almost every chapter which involves angles. Sometimes the student may get confused when the angle is given in radians, so just to clarify he can convert it into degrees and then move ahead with the sum. It is vital that the student converts from radians to degrees in most of the numerical related to the chapter of Heights and distances, curves in order to simplify the sum and apply the formula appropriately.