How do you determine the quadrant in which (7pi)/5 lies?

1 Answer
Ben
Mar 8, 2018

Quadrants are broken up into regions of pi/2, so if you calculate the smallest multiple of pi/2 that is larger than your angle, you can determine the quadrant (3rd quadrant for this one)

Explanation:

I'm referring to quadrants as q1, q2, q3, and q4 for brevity:

if traveling around a unit circle is 2pi radians, then the quadrants would be 1/4 of that angle... or pi/2 for each quadrant.

q1 would range from 0 to pi/2
q2 would range from pi/2 to pi
q3 would range from pi to (3pi)/2
q4 would range from (3pi)/2 to 2pi

to make these comparable to the desired angle, both the value of (7pi)/5 and the quadrant values need to be brought to their lowest common denominator. In this case, that is 10.

angle: (14pi)/10

we know that 14/10 is greater than 1, so we can eliminate q1 and q2 from the possible answers. This leaves us with q3 and q4:

q3: (10pi)/10 harr (15pi)/10
q4: (15pi)/10 harr (20pi)/10

Since 14 is less than 15, we can conclude that it is the third quadrant.

Related questions
See all questions in Measuring Rotation
Impact of this question
7087 views around the world
You can reuse this answer
Creative Commons License