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Coterminal Angle Calculator

degree

/

radian

rotating circle




least 
angle coterminal with
(




least 
angle coterminal with
(
)
Solution:  
°

 or 

°

Only Two Values Required


Coterminal Angle Tutorial


Coterminal angles are angles that share the same initial and terminal sides. To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians. If told to find the least positive angle coterminal with 785 degrees you can use the following calculation process shown below. The maximum amount of times 360 degrees can be subtracted from 785 degrees and stay positive is found by dividing the given angle, 785 degrees and dividing it by 360 but rounding down to the closet whole number. This number is 2. Once that number is found, it is multiplied by 360 and subtracted from 785 degrees. If told to find the least negative angle coterminal with 526 degrees, a similar calculation process would be used with the only difference being that the dividend of the given Angle and 360 degrees must be added up. Once this number is found, it must again get subtracted from the given angle 526 degrees. This gives you the least negative coterminal angle. Finding angles coterminal with radian values can be done the same way. If told to find the least positive angle coterminal with 32 pi radian you would use the calculation process below: Since the least positive value if being calculated the dividend of the given radian and 2pi must be rounded down to a whole number. This whole number must them be multiplied by 2 pi and subtracted from the given value. This results in the solution, pi. But you To find the least negative angle coterminal with another angle, say 78 pi, the calculation process is shown below will work. In this case, the smallest negative angle is needed meaning the dividend of 78 pi and 2 pi must get rounded up to the nearest whole number. This number must then get subtracted from the 78 pi for the solution to be found.