Question

How do you convert 36 degrees to radians?

Answer 1

Hint : To convert any value of degree into radians, we will multiply the degree value with $\pi$ and then divide it by 180. Which can be mathematically described as:-
$f = x \times \left( {\dfrac{\pi }{{180}}} \right)$ , where f is the value of degree in radians and x is the amount in degrees. After you have multiplied the given values with respect to the formula above you will get $\dfrac{{36}}{{180}}\pi$ as the answer. But to simplify the answer more, we will divide both numerator and denominator by 36 which will give us our most simplified answer that is $\dfrac{\pi }{5}$ .

Complete step-by-step answer :
The given value of degrees in the question is 36 and we know that in order to convert 36 degrees into radians, there is one mathematical formula which is given by:-
If $x$ is the amount of degrees needed to be converted into radians and let $f$ is the radian equivalent of x, then,
$f = x \times \left( {\dfrac{\pi }{{180}}} \right)$
Therefore, putting the value of x in the above equation, we will get
$f = 36 \times \left( {\dfrac{\pi }{{180}}} \right) \\\ = \dfrac{{36\pi }}{{180}} \\\ = \dfrac{{36}}{{180}}\pi \;$
So to simplify our answer more, we will further divide each numerator and denominator by 36, to get the smallest and most simplified possible answer
$\dfrac{{\dfrac{{36}}{{36}}}}{{\dfrac{{180}}{{36}}}} \times \pi = \dfrac{1}{5} \times \pi \\\ = \dfrac{\pi }{5} \;$
Therefore, the radian equivalent of 36 degrees is $\dfrac{\pi }{5}$ radians
So, the correct answer is “ $\dfrac{\pi }{5}$ radians”.

Note : If you want to get a further simplified answer in decimal numbers then use the value of $\pi$ that is 3.14 and divide it by 5 to get the required decimal digits.
Hence, 36 degrees is equal to 0.628 radians.