Question

How do you convert $36$ degrees into radians?

Answer 1

Hint: To convert degree to radians we have a formula, which is given by: $x\deg ree = \dfrac{\pi }{{180}}xradians$. Now in place of $x$ substitute the value in terms of degree, they have given and solved for the correct answer. That is by simply multiplying the degree they have given with $\dfrac{\pi }{{180}}$ you will get the required answer in terms of radians.

Complete step by step answer:
In the question they have given in terms of degree, that is $36$ degrees.
They have asked to find the $36$ degrees in terms of radians.
So to convert degree to radians we have a relation between degree and radians given by:
$x\deg ree = \dfrac{\pi }{{180}}x \text{ radians}$
By using the above relation we need to find the required answer.
From the above relation, it is clear that one degree is equal to $\dfrac{\pi }{{180}}$ radians, that is if we substitute one in place of $x$ in the relation equation.
Now, to calculate $36$ degrees in terms of radians, just multiply $36$ with $\dfrac{\pi }{{180}}$ to arrive at the required answer.
Therefore, we can write as
${36^ \circ } = 36 \times \dfrac{\pi }{{180}}radians$
Both $180$ and $36$ are divisible by $36$ so on simplification, we get
${36^ \circ } = \dfrac{\pi }{5}radians$ or ${36^ \circ } = 0.628radians$

Therefore, the $36$ degrees can be written as $\dfrac{\pi }{5}$ or $0.628$ radians.

Note:
In this conversion type problem, one thing we need to remember is the conversion formula. If you feel like this is a lengthy process whenever they ask to convert the degree to radian, directly divide the value given in terms of degree by $180$ and reduce that to its lowest terms. Then finally multiply the answer or the result you got by $\pi $ you will get the same answer.