Yes, except at odd multiples of pi/2 radians, where the cosine is zero so that the division is not defined.
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Cotangent is 1 / tangent. Since tangent is sine / cosine, cotangent is cosine / sine.
in trigonometry
The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.
If you know the angle's sine, cosine, or tangent, enter it into the calculator and press <inverse> sine, cosine, or tangent. On MS Calc, in Scientific Mode, using Degrees, enter 0.5, then check Inv and the press sin. You should get 30 degrees. The other functions work similarly.
sine, cosine, tangent, cosecant, secant and cotangent.