What is the radian measure of a right angle?

2 Answers
May 11, 2018

90 degrees=pi/2 radians

Explanation:

Radians are a unit measure for angles defined as the ratio between the lenght of an arc of circumference and the radius of the circumference itself.

This image from wikipedia explains it quite well: upload.wikimedia.org

and this gif helps you understainding why an angle of 180 degrees translates into pi radians, and an angle of 360 degrees translates into 2pi radians:
upload.wikimedia.org

That being said, we only need to use some proportions: since a right angle measures 90 degrees, it is half of a 180 degrees angle. We already observed that an angle of 180 degrees translates into pi radians, and thus an angle of 90 degrees translates into pi/2 radians (we simply divided by 2 both the degrees and radians).

May 11, 2018

We have a very goofy system where our circle constant pi is half a circle, 180^circ, so a right angle, one quarter of a circle, 90^circ, is half the circle constant, pi/2. Confused yet?