Question

What is $67.5$ degrees in terms of radians?

Answer 1

Hint: In this problem we need to convert the given degrees into radians. We know that $180$ degrees can make one radian that means one radian is equal to $180$ degrees. Mathematically we can write it as $1\pi \text{ radians}=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 $67.5$ degrees into radians. So, we will multiply $67.5$ with the number of radians per one degree to get the required result.

Complete step-by-step answer:
Given angle $67.5$.
We can say the relation between degree and radian as one radian is equal to $180$ degrees. Mathematically we can write it as
$\pi =180{}^\circ $
Dividing the above equation with $180$ on both sides to get the number of radians per one degree, then we will get
$\dfrac{\pi }{180}=\dfrac{180{}^\circ }{180}$
We know that $\dfrac{a}{a}=1$. Using this formula in the right-hand side of the above equation and isolating the equation, then we will have
$1{}^\circ =\dfrac{\pi }{180}$
From the above equation we can say that one degree of angle is equal to $\dfrac{\pi }{180}$ radians. So, to convert $67.5$ into radians we will multiply with $67.5$ on both sides of the above equation, then we will get
$67.5\times 1{}^\circ =67.5\times \dfrac{\pi }{180}$
Simplifying the above equation by applying basic mathematical operations, then we will have
$67.5{}^\circ =\dfrac{3}{8}\pi $
Hence the $67.5$ is equal to $\dfrac{3}{8}\pi $ radians.

Note: In this problem we have used the relation between the degrees and radians as $\pi =180{}^\circ $. There is also another equation which gives the relation between the degrees and radians which is $2\pi =360{}^\circ $. We can use any one of the equations according to our convenience.