Question

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

Answer 1

Hint: Here convert the given radians into degrees, and this can be converted using the conversion formula i.e., $xrad=x\times {\displaystyle \frac{{180}^o}{\pi }}$ 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 ${\displaystyle \frac{3\pi }{4}}$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, $1rad={\displaystyle \frac{{180}^o}{\pi }}$,
Now using the formula $xrad=x\times {\displaystyle \frac{{180}^o}{\pi }}$ we can convert ${\displaystyle \frac{3\pi }{4}}$ radians into degree, here $x={\displaystyle \frac{3\pi }{4}}$,
By substituting the value of $x$ in the formula, we get,
$\Rightarrow {\displaystyle \frac{3\pi }{4}}radian={\displaystyle \frac{3\pi }{4}}\times {\displaystyle \frac{{180}^o}{\pi }}$ degree,
By eliminating the like terms we get,
$\Rightarrow {\displaystyle \frac{3\pi }{4}}radian={\displaystyle \frac{3}{4}}\times {180}^o$ degrees,
Now simplifying we get,
$\Rightarrow {\displaystyle \frac{3\pi }{4}}radian=3\times 45$ degrees,
Again multiplying we get,
$\Rightarrow {\displaystyle \frac{3\pi }{4}}radian=135$ degrees,
The converted degree is 135 degrees.

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

Note: Do not mistake with the formula for conversion of angle to radians as, $1rad={\displaystyle \frac{{360}^o}{\pi }}$ degrees, as it is a wrong formula, Only if ${360}^0=2\pi$ then we can write it as, $1rad={\displaystyle \frac{{360}^o}{2\pi }}={\displaystyle \frac{{180}^o}{\pi }}$ 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.