Question

How do you convert 225 degrees into radians?

Answer 1

Hint: In the above question we were asked to convert 225 degrees into radian. Radian is a measurement based on the radius of the circle. Also, in a half-circle, there are $\pi$ radians that are ${180^ \circ }$. You can convert degrees into radian by multiplying it to $(\dfrac{\pi }{{180}})$. So let us see how we can solve this problem.

Complete Step by Step Solution:
In the given question we were asked to convert 225 degrees into radian.
We can convert degrees into radian by multiplying it to $(\dfrac{\pi }{{180}})$ . Therefore, multiplying 225 degrees with $(\dfrac{\pi }{{180}})$
 $= ({225^ \circ }) \times (\dfrac{\pi }{{180}})$
 $= (\dfrac{{225}}{{180}}) \times (\pi )$ radians
After dividing numerator and denominator we get,
 $= 1.25\pi$ radians
 $= 3.925$ radians

3.925 radians is nearly equal to
 $\approx 3.93$ rad

Note:
In the above solution, we get $1.25\pi$ radians after dividing 225 with 180. Note that the value of $\pi$ is 3.141 which we get after dividing 22 with 7. Also, for converting degrees into radians we need to multiply the degree with $(\dfrac{\pi }{{180}})$ but for converting radian into degrees we need to multiply radian with $(\dfrac{{180}}{\pi })$. And the value of $\pi$ is fixed which is 3.141 or $\dfrac{{22}}{7}$.