How this calculator works
Cotangent divides the horizontal coordinate by the vertical coordinate. Its graph decreases between consecutive multiples of 180°, where sine is zero and vertical asymptotes occur. At 90° cosine is zero but sine is one, giving a valid zero. Using cos θ/sin θ directly handles this case better than trying to invert an undefined tangent. There is no finite amplitude. Ratio mode uses arccotangent on (0°, 180°), including obtuse results for negative inputs.
Formula
cot θ=cos θ/sin θ=adjacent/opposite; cot(θ+π)=cot θ; cot(-θ)=-cot θ. cot 90°=0 even though tan 90° is undefined.
Worked example
cot 45°=1 and cot 30°=√3. A cotangent of -1 corresponds to 135° under the chosen branch. At 90° cotangent is zero.
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Frequently asked questions
Why is cot 90° defined?
Its denominator is sin 90°=1 and its numerator is cos 90°=0, so the quotient is zero.
Is cotangent always 1/tangent?
Where both expressions are defined, yes. The cosine-over-sine definition also defines cotangent at angles where tangent is undefined.
Which inverse convention is used?
Arccotangent returns an angle strictly between 0° and 180°. Some software uses another convention for negative inputs.