Answer:
-161.57°, or 198.43°
Step-by-step explanation:
The third-quadrant angle can be found using the usual rectangular-to-polar conversion. The angle is given by ...
θ = ATAN2(x, y) = ATAN2(-12, -4) ≈ -161.57°
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More conventionally, the reference angle is ...
tan(θ) = y/x = -4/-12 = 1/3
θ = arctan(1/3) ≈ 18.43° . . . . angle from -x axis (CCW)
Since this is a 3rd-quadrant angle, the positive angle value will be 180° plus the reference angle:
180° +18.43° = 198.43°
The angle most directly measured from the +x axis is ...
360° -198.43° = -161.57°
