Question

Convert 37 degrees to radian?

Answer 1

Hint: In this question we are asked to convert the given degree into radians, and this can be converted using the conversion formula i.e.,$x^{\circ }=x^{\circ }\times {\displaystyle \frac{\pi }{{180}^{\circ }}}$ radians, and substituting the number of degrees i.e.$x$ in this formula we will get the required converted radians.

Complete step-by-step solution:
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. ${360}^{\circ }$ (360 degrees) is equal to$2\pi$radians.
 Given degree is 37,
We have to convert the degree into the radians, by using the conversion formula.
We know that ${180}^{\circ }=\pi$ radians, then we can write 1 degree as,$1^{\circ }={\displaystyle \frac{\pi }{{180}^{\circ }}}$,
Now using the formula $x^{\circ }=x^{\circ }\times {\displaystyle \frac{\pi }{{180}^{\circ }}}$ we can convert 37 degrees into radians, here $x={37}^{\circ }$,
By substituting the value of $x$ in the formula, we get,
$\Rightarrow {37}^{\circ }={37}^{\circ }\times {\displaystyle \frac{\pi }{{180}^{\circ }}}$,
By simplifying we get,
$\Rightarrow {37}^{\circ }={\displaystyle \frac{37\pi }{180}}$ radians.

$\therefore$The radians form when we convert 37 degrees to radians is equal to ${\displaystyle \frac{37\pi }{180}}$.

Note: There is a chance that students can make mistake while solving these type of questions in taking formula for conversion of angle to radians as,$1^{\circ }={\displaystyle \frac{\pi }{{360}^{\circ }}}$ radians, as it is a wrong formula a ${360}^{\circ }=2\pi$ then we can write it as,$1^{\circ }={\displaystyle \frac{2\pi }{{360}^{\circ }}}={\displaystyle \frac{\pi }{{180}^{\circ }}}$ radians. ${360}^{\circ }=2\pi$ .
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.