Question

How do you convert $30{}^\circ$ into radians?

Answer 1

Since we know a relation between degree and radian that is $360{}^\circ$ equals to $2\pi$ radians that is $360{}^\circ =2\pi$ then we calculate the radians in $1{}^\circ$ and then multiply it with the $30{}^\circ$ degrees that we want to convert in radians.

Complete step-by-step answer:
Since we know that $360{}^\circ =2\pi$
$\Rightarrow \pi =180{}^\circ$
Now will calculate the radians in unit degree
$\Rightarrow 1{}^\circ =\dfrac{\pi }{180}radian$
Now the radians in $30{}^\circ$ , for this we need to multiply the radian in unit degree with $30{}^\circ$
$\Rightarrow 30\times \dfrac{\pi }{180}$
$\Rightarrow \dfrac{\pi }{6}$
Thus we have converted the $30{}^\circ$ into radians
Hence, $30{}^\circ =\dfrac{\pi }{6}radian$

Note: Whenever we see the angles in degrees and want to convert into radians just replace $180{}^\circ$ with $\pi$ and it is suggested to use the radian system that means be familiar with angles in terms of $\pi$ as this will help we in our further topics like calculus and inverse trigonometry and in the physics too.