Type a value for the angle like: 60, 30, 1/3, 3/2, etc. 
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Calculator useTo use this calculator, just type a value for the angle. You may choose radians (rad) or degrees (°) as the angle unit. The default unit is degree (°) Examples of accepted input values
Note: this calculator accepts numbers, fractions, 'pi', 'π', '+', '', '*', '/', '(', ')' and some (not all) combinations of them as input. Use it with care! 
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Short answer 
How to find reference angle of 31π/90 
The reference angle is the angle that the given angle makes with the xaxis. Regardless of the location of the terminal side of the angle, the reference angle measures the closest distance of that terminal side to the xaxis.
Reference angles always have positive measures. Since their measures add up to 180 degrees, each of the references should measure less than 180°.
When the terminal side is in the first quadrant (angles from 0° to 90° or from 0 to π/2), the reference angle is the same as the given angle. So, if our given angle is 60°, then its reference angle is also 60°.So, you can use this formula.
Reference angle° = angle
When the terminal side is in the second quadrant (angles from 90° to 180° or from π/2 to π), our reference angle is 180° minus our given angle. So, you can use this formula.
Reference angle° = 180  angle
For example:
The reference angle of 125 is 180  125 = 55°.
When the terminal side is in the third quadrant (angles from 180° to 270° or from π to 3π/4), our reference angle is our given angle minus 180°. So, you can use this formula.
Reference angle° = 180  angle
For example:
The reference angle of 190 is 190  180 = 10°.
When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle. So, you can use this formula.
Reference angle° = 360  angle
For example:
The reference angle of 290 is 290  180 = 70°.