Explanation:
Consider the quadrant of the original angle and where half that angle would lie.
Half of any positive 1st- or 2nd-quadrant angle will lie in the first quadrant.
Half of any positive 3rd- or 4th-quadrant angle will lie in the second quadrant.
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Half of any negative 1st- or 2nd-quadrant angle will lie in the third quadrant.
Half of any negative 3rd- or 4th-quadrant angle will lie in the fourth quadrant.
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Here, we are using the wording "x-quadrant angle" to mean an angle whose terminal ray lies in the x-quadrant. The measure of that angle may be positive or negative. (Half of -5π/4 radians will have different trig function values than half of +3π/4 radians, even though they both have their terminal ray in the 2nd quadrant.)
We are assuming the angle does not exceed 360° (or 2π radians). If it does, you need to adjust the half-angle quadrant accordingly.
