Identify Quadrant of Angle (radians)

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SUMMARY

The discussion focuses on determining the quadrant of an angle given in radians without converting to degrees. For the angles -1 and -2 radians, the calculations show that -1 radians corresponds to Quadrant IV, while -2 radians corresponds to Quadrant III. The participants emphasize the importance of understanding the radian equivalents of key angles, specifically 0, π/2 (approximately 1.57), π (approximately 3.14), and 3π/2 (approximately 4.71), to identify quadrants directly in radians.

PREREQUISITES
  • Understanding of radians and their relationship to degrees
  • Knowledge of the unit circle and angle quadrants
  • Familiarity with basic trigonometric concepts
  • Ability to perform angle conversions between radians and degrees
NEXT STEPS
  • Study the unit circle and its significance in trigonometry
  • Learn how to convert between radians and degrees accurately
  • Explore the properties of angles in different quadrants
  • Investigate trigonometric functions and their values in various quadrants
USEFUL FOR

Students studying trigonometry, educators teaching angle measurement, and anyone needing to understand the relationship between radians and angle quadrants.

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Homework Statement



Determine the quadrant in which the terminal side of the angle lies. (The angle is given in radians.)

a) -1 b) -2

The Attempt at a Solution



a) -1 * (180/3.14) = -57.3 degrees -- Quadrant IV

b) -2 * (180/3.14) = -114.6 degrees -- Quadrant III

- Is there a way to find out which quadrant they're in without having to to convert them into degrees?
 
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Well, how does knowing them in degrees help you? I assume it is because you know that 0, 90, 180, and 270 degrees, as well as -90, -180, and -270 are the "separators". You should know the same thing for radians. The corresponding values are 0, \pi/2= 0.785, \pi/2= 1.57, 3\pi/2= 4.71, and the corresponding negative values.
 

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