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Determine which quadrant a angle is in when given radians - math tutorial

1,914 views · Published 12 December 2011 · 2:27 · Indexed 18 October 2026

Channel: Brian McLogan · 2011 · Education

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👉 Learn how to determine the quadrant of an angle given in radians. Recall that 1 radian is the distance on the circumference of the circle that is equivalent to the radius of the circle. Also, recall that the circumference of a circle is equivalent to 2pi radians.

To determine the quadrant of the angle in radians written in terms of pi, we divide the top half and the bottom half of the circumference of the circle into the number of parts corresponding to the denominator of the radian angle. Then we count from the positive x-axis in an anti-clockwise direction for positive angles and in the clockwise direction for negative angles the number of parts corresponding to the coefficient of pi in the numerator.

The quadrant where the number of parts corresponds to the coefficient of the pi in the numerator of radian angle is the required quadrant.

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Organized Videos:
✅ Angles in Trigonometry
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrdn9zTKTFo5MayxpoQkKWB
✅ Solve Problems with Arc Length
https://www.youtube.com/playlist?list=PL0FAA8F3A4A64C0CD
✅ Angles in Trigonometry | Learn about
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpqCJQreDI0Q7ibZ-q8pQ8v
✅ Sketch Angles in Standard Position
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqYCdsQY6BeWuw4GIxNq-Ps
✅ Find the Quadrant of the Angle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMquYefa135efFiGsBTEMwZY
✅ Find the Reference Angle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpxWekQ0Nll5aeJRLj8IAcS
✅ Complement and Supplement of an Angle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMocTFwM1FKKocsENTOyFjMe
✅ Convert Radians to Degrees 
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqaSH_QGSKbBFVkIZn63I74
✅ Convert Degrees to Radians
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMppuYwc90qqVM-EtIIfu0KJ
✅ Convert Degrees to Degree Minute Seconds
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoAVUc0hQVM9F2mtTZ5zIXP
✅ Convert Degree Minute Seconds to Degrees
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrZmQzUM7FeVAsKtYOqM8VT
✅ Coterminal Angles | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoqhYuu6l44dkl97jg3V62_
✅ Find Coterminal Angles | 0 and 2pi
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrJJVmzS9g-s6nDoIXrIR2l
✅ Find Coterminal Angles | 0 and 360
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoA7QwPW6Wd78ePabiyQwOZ

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