Question

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

Answer 1

Hint: 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.