replace -230° by 130° (-230° + 360° = 130°) and observe that the angle is in the 2nd quadrant. So, the reference angle is the acute angle between the terminal side of the angle 130° and the negative x-axis (180°).

At first, you need to determine in which quadrant is the angle. If it is positive but large than 360°, you may subtract an appropriate multiple of 360° and then choose the reference angle:

If the angle is in the 1st quadrant, then nothing else should be done e.g, ref. angle for 45° is 45°).

If the angle is in the 2nd quadrant, subtract it from 180° (as in the given example).

If the angle is in the 3rd quadrant, subtract 180° from it (e.g., ref. angle for 250° is 70°).

If the angle is in the 4th quadrant, subtract it from 360° (e.g., ref.angle for 300° is 60°)

May 2nd, 2015

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