If you are familiar with trigonometric functions defined in terms of the unit circle, the x and y coordinates are negative in the third quadrant. As a result, x/y, the ratio that defines cotangent, is positive.
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The tangent and cotangent functions.
Cotangent(0.675 radians) = 84.88 approx.
The cotangent of 510 degrees is: -1.73205081
Tangent and cotangent positive; other 4 negative.
1/(tangent of angle)