Reference Angle Calculator

Enter the original angle into the calculator to evaluate the reference angle. The reference angle is also known as the acute angle, or smallest angle made between the angle and the x-axis.

Reference Angle Formula

The reference angle for any angle for any angle can be calculated through the following formula:

RA = ABS (180-x)

  • Where RA is the reference angle in degrees
  • X = the original angle in degrees
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Reference angles are typically used in trigonometric theorem problems. They help solve proofs for the trig functions. In general, when someone is looking for a reference angle, they have a given angle theta to start with. The key to solving a reference angle is to understand which quadrant the angle lies in.

How to calculate a reference angle

The following is a step by step guide on how to calculate the reference angle of any angle.

  1. First, the standard or original angle must be measured or calculated. For this example we will assume the use of a protractor to measure an angle of 120 degrees.
  2. Next, the quadrant that this angle lays in must be determined. The quadrant that an angle is in changes every 90 degrees. Therefore, this angle would be in the second quadrant.
  3. Finally, the angle must be put into the formula above to calculate the reference angle. So RA = ABS (180-120) = ABS (60) = 60. We find that the reference angle is 60 degrees.
  4. Analyze these results and check using the graphic above to make sure it lies in the correct quadrant.
reference angle calculator

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