How to find the reference angle for any angle not on the unit circle
Answer 1
Charlotte Davis
To find the reference angle for an angle θ not on the unit circle, you must first locate the angle in the appropriate quadrant. The reference angle is then the smallest angle between the terminal side of θ and the x-axis. Here are the steps:
1. If θ is in the first quadrant, the reference angle is θ itself:
$ θ_{ref} = θ $
2. If θ is in the second quadrant, the reference angle is:
$ θ_{ref} = 180° – θ $
3. If θ is in the third quadrant, the reference angle is:
$ θ_{ref} = θ – 180° $
4. If θ is in the fourth quadrant, the reference angle is:
$ θ_{ref} = 360° – θ $
Answer 2
Daniel Carter
To find the reference angle for an angle θ not on the unit circle:
1. If θ is in the first quadrant, the reference angle is θ:
$ θ_{ref} = θ $
2. If θ is in the second quadrant, the reference angle is:
$ θ_{ref} = 180° – θ $
3. If θ is in the third quadrant, the reference angle is:
$ θ_{ref} = θ – 180° $
4. If θ is in the fourth quadrant, the reference angle is:
$ θ_{ref} = 360° – θ $
Answer 3
Chloe Evans
To find the reference angle for an angle θ not on the unit circle:
1. First quadrant: $ θ_{ref} = θ $
2. Second quadrant: $ θ_{ref} = 180° – θ $
3. Third quadrant: $ θ_{ref} = θ – 180° $
4. Fourth quadrant: $ θ_{ref} = 360° – θ $
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