Question

What is the radian measure of a right angle?

Answer 1

We have two methods of measuring an angle in degrees and in radian. Radian is another way of expressing the measure of an angle. In this question we have to calculate the radian measure of a right angle i.e., radian measure of $90^\circ$.

Complete step by step answer:
Radian measure of a central angle of a circle is defined as the ratio of length of the arc subtended by that angle to the length of the radius of the circle. A radian is represented by the symbol rad.
The system of radians for measuring the angles is much more mathematically pure than degrees.
Here we have to find the radian measure of right angle i.e., $90^\circ$
According to the definition, the radian measure of an angle is written as the ratio of length of arc $l$ subtended by the central angle $\theta$ to the radius $r$.
So, we can write the above statement as $\theta = \dfrac{l}{r}$
Now, let us take a semicircle, we know that the central angle subtended by a semicircle is $180^\circ$ and when we calculate the number of radians required to represent the central angle of a semicircle it is equal to $3.1415$ approximately which is equal to $\pi$
So, $\pi$ radian is equal to $180$.
We know that $90^\circ$ is the half of $180^\circ$
If $\pi$ radian is equal to $180$, then
$\Rightarrow 90^\circ = \dfrac{\pi }{2}$
Hence the radian measure of right angle is $\dfrac{\pi }{2}$.

Note:
Keep in mind the basic difference that the radian measure relates to the arc length and radius of a circle whereas the degree measure relates the circumference and diameter of the circle. If we want to convert degree into radians, we will multiply the angle by $\dfrac{\pi }{{180}}$ and if we want to convert radian into degree, we will multiply the angle by $\dfrac{{180}}{\pi }$.