Question

Convert $\dfrac{{3\pi }}{4}$ radians to degrees?

Answer 1

Hint: Here convert the given radians into degrees, and this can be converted using the conversion formula i.e., $xrad = x \times \dfrac{{{{180}^o}}}{\pi }$ degrees, and substituting the number of radians i.e., $x$ in this formula we will get the required converted degrees.

Complete step by step answer:
Degrees and radians are ways of measuring angles. A radian is equal to the amount an angle would have to be open to capture an arc of the circle's circumference of equal length to the circle's radius. ${360^0}$ (360 degrees) is equal to radians.
 Given radian is $\dfrac{{3\pi }}{4}$rad,
We have to convert the radian into the degrees, by using the conversion formula.
We know that ${180^0} = \pi $radians, then we can write 1 radian as, $1rad = \dfrac{{{{180}^o}}}{\pi }$,
Now using the formula $xrad = x \times \dfrac{{{{180}^o}}}{\pi }$ we can convert $\dfrac{{3\pi }}{4}$ radians into degree, here $x = \dfrac{{3\pi }}{4}$,
By substituting the value of $x$ in the formula, we get,
$ \Rightarrow \dfrac{{3\pi }}{4}radian = \dfrac{{3\pi }}{4} \times \dfrac{{{{180}^o}}}{\pi }$ degree,
By eliminating the like terms we get,
$ \Rightarrow \dfrac{{3\pi }}{4}radian = \dfrac{3}{4} \times {180^o}$ degrees,
Now simplifying we get,
$ \Rightarrow \dfrac{{3\pi }}{4}radian = 3 \times 45$ degrees,
Again multiplying we get,
$ \Rightarrow \dfrac{{3\pi }}{4}radian = 135$ degrees,
The converted degree is 135 degrees.

The degree form when we convert $\dfrac{{3\pi }}{4}$ radians to degrees is equal to 135 degrees.

Note: Do not mistake with the formula for conversion of angle to radians as, $1rad = \dfrac{{{{360}^o}}}{\pi }$ degrees, as it is a wrong formula, Only if ${360^0} = 2\pi $ then we can write it as, $1rad = \dfrac{{{{360}^o}}}{{2\pi }} = \dfrac{{{{180}^o}}}{\pi }$ degrees.
Degrees are more common in general: there are 360 degrees in a whole circle, 180 degrees in a half circle, and 90 degrees in a quarter of a circle. A radian is the amount an angle has to open such that the length of the section of the circle's circumference it captures is equal to the length of the radius.