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.,${x^\circ} = {x^\circ} \times \dfrac{\pi }{{{{180}^\circ}}}$ 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,${1^\circ} = \dfrac{\pi }{{{{180}^\circ}}}$,
Now using the formula ${x^\circ} = {x^\circ} \times \dfrac{\pi }{{{{180}^\circ}}}$ 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 \dfrac{\pi }{{{{180}^\circ}}}$,
By simplifying we get,
$ \Rightarrow {37^\circ} = \dfrac{{37\pi }}{{180}}$ radians.

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

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,${1^\circ} = \dfrac{\pi }{{{{360}^\circ}}}$ radians, as it is a wrong formula a ${360^\circ} = 2\pi $ then we can write it as,${1^\circ} = \dfrac{{2\pi }}{{{{360}^\circ}}} = \dfrac{\pi }{{{{180}^\circ}}}$ 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.