We are already familiar with measuring angles in degrees. But we can also measure angles using radians.
One radian is the measurement of an angle, formed at the center of a circle, that makes an arc whose length is the same as radius.
Let’s break it down:
One radian is the measurement of an angle
formed at the center of a circle
that makes an arc
whose length is the same as radius.
Here, angle a is equal to 1 radian. We can simply denote radians as 'rad’.
Assume that the radius of our circle is 1 unit (centimetre, metre, whatever). Now if you walk the distance of 1 unit on the circumference, the measurement of the angle will be 1 rad. If you walk 2 units, it will be 2 rad. So if you walk the whole circumference, what will be the measurement of the angle (in radians)? The distance you traveled will be 2π units.(since circumference = 2πr and r is 1 units here), which means that the angle will be 2π rad.
How to convert between degrees and radians?
The angle formed by the complete circle is 360° or 2π rad (radians). This means that 360° = 2π rad.
360° = 2π rad
=> 180° = π rad
=> (180/π)° = 1 rad OR 1° = (π/ 180) rad
Example 1
Convert 75 degrees to radians.
Example 2
Convert 1.5π radians to degrees.
