What is the radian measure of a right angle?

2 Answers
KillerBunny
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).

Dean R.
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?

Related questions
See all questions in Radian Measure
Impact of this question
12011 views around the world
You can reuse this answer
Creative Commons License