This angle should be in the standard position. The vertex is fixed to the origin of the graph and the initial side, where the angle starts opening, runs along the x-axis. [2] X Research source

The formula can be written as θ±360°, where θ is your original angle. For example, if your original angle was 30°, you may write 30° + 360°. The resulting coterminal angle would then be 390°, or 13π/6 rad if you need to convert to radians. Adding one revolution would be considered the smallest positive coterminal angle. [4] X Research source This also applies to radians.

If your θ is π/6 rad, you may set up the problem as π6 - 2π. The resulting coterminal for this equation is -11π/6 rad, or -330° if you need to convert to degrees. Subtracting one revolution would be considered the smallest negative coterminal angle. [6] X Research source This applies when working with degrees, as well.

This formula can be written as θ+360x and θ+2πx, where θ is your original angle and x is the amount of times you need to rotate. If your original angle was 52°, adding 360° twice will give you 412° and 772°. Taking the same angle, 52°, subtracting 360° twice will return -308° and -668°. You can also add and subtract from the same angle to get more than one coterminal. This works great if you need to find both a positive and a negative coterminal angle. For instance, if you need to find a positive and negative coterminal of π/4, adding 2π will give you the positive result 9π/4 rad and subtracting will give you the negative -7π/4 rad.

If your original angle is 361°, the least positive coterminal angle will be 1°. Subtracting anymore will result in negative angles. Alternatively, the “least positive” will be the first coterminal greater than 0 if your original angle is negative. Your original angle could be -250°. The least positive coterminal would then be 110°, which is found by adding one revolution.

For the starting angle 3π/4 rad, the most negative coterminal angle would be -5π/4 rad. This is found by subtracting 2π rad once, which gives a negative angle. If your starting angle is already negative, the last negative coterminal before your cross 0 would be the most negative. Let’s say your original angle is -17π/4 rad. The most negative coterminal would be -π/4 rad, which is found by adding 2π twice. Adding another 2π would push you into the positives.