Question

How do you convert $270$ degrees to radians?

Answer 1

Here we have to convert the degree to radian. For this conversion we will use a relation between degrees and radians. The relation is $X^\circ = \dfrac{{\pi X}}{{180}}radians$. Now on putting the value of X in degree and further simplifying it, we get the required answer in radians.

Complete step by step solution:
In the given question we have to convert 270 degrees into radians.
To convert we use the relation between degrees and radians.
The relation between degrees and radians
$X^\circ = \dfrac{{\pi X}}{{180}}radians$
From the above relation it is clear that $1$ degree is equal to $\dfrac{\pi }{{180}}radian$.
So for getting $270^\circ$ into radian we have to put $270$ in the place of ‘X’
On putting this value in the above relation we get
$270^\circ = \dfrac{{\pi \times 270}}{{180}}radians$
On further simplify we get
$270^\circ = \dfrac{{3\pi }}{2}radians$
Hence, the $270$ degrees can be written as $\dfrac{{3\pi }}{2}$ radians.

Note:
Degrees and radians are two different units that are used for the measurement of the angles. The conversion of degrees to radians is used while measuring the angle in geometry.
The measure of the angle generally denoted in degrees having the symbol $( \circ )$and an angle can be measured by two units that are degrees and radian. But for solving this type of problem we should remember conversion formulas.