Question

How do you convert $110$ degrees into radians.

Answer 1

We know that the degree and radians are the measurement of angle. In this problem we need to convert the degrees into radians. We know that one radian is equal to $180$ degrees. Mathematically we can write it as $\pi =180{}^\circ$. From this relation we will calculate one degree is equal to how many radians by dividing the above equation with $180$ on both sides. Now we need to convert $110$ degrees into radians. So, we will multiply $110$ with the number of radians per one degree to get the result.

Complete step-by-step solution:
Given angle $110{}^\circ$.
We know that one radian is equal to $180$degrees. Mathematically, we can represent it as
$\pi =180{}^\circ$
Dividing the above equation with $180$ on both sides, then we will get
$\dfrac{\pi }{180}=\dfrac{180{}^\circ }{180}$
We know that $\dfrac{a}{a}=1$, then we will get
$\Rightarrow 1{}^\circ =\dfrac{\pi }{180}$
From the above equation we can say that one degree is equal to $\dfrac{\pi }{180}$ radians. So, to convert $110{}^\circ$ into radians we will multiply with $110$ on both sides of the above equation, then we will get
$\Rightarrow 110\times 1{}^\circ =110\times \dfrac{\pi }{180}$
Simplifying the above equation, then we will get
$\Rightarrow 110{}^\circ =\dfrac{11}{18}\pi$
Hence the $110{}^\circ$ is equal to $\dfrac{11}{18}\pi$ radians.

Note: In this problem they have asked to convert the degrees into radians, so we have followed the above procedure. If they have given radians and asked to convert it into degrees, then we will use the equation $\pi =180{}^\circ$ and simplify to get the result.