Cotangent Calculator

The cotangent (cot) of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the opposite side. Alternatively, in the unit circle framework, cotangent is the reciprocal of the tangent function and equals the cosine of the angle divided by its sine: cot(theta) = cos(theta) / sin(theta). When you input an angle, the tool evaluates this trigonometric identity to return an exact numeric output, while automatically translating between radians and degrees to match your preferred measurement scale.

Let us calculate the cotangent of an angle measuring 45 degrees. First, convert the degree measurement into radians if required by the formula, though standard evaluation yields a direct ratio. For 45 degrees (which is pi/4 radians), the sine and cosine values are both equal to approximately 0.7071. Applying the cotangent formula, cot(45 degrees) = cos(45 degrees) / sin(45 degrees) = 0.7071 / 0.7071 = 1. Thus, the cotangent for a 45-degree angle is precisely 1, demonstrating a symmetrical balance between the adjacent and opposite sides of the reference triangle.

Always double-check whether your input is set to degrees or radians before running your calculation, as mixing these units will yield incorrect results. Be mindful of undefined values; for angles where the sine equals zero (such as 0 degrees, 180 degrees, or multiples of pi), the cotangent approaches infinity or negative infinity because division by zero is undefined. Keep a unit circle handy to quickly verify the sign of your cotangent result depending on the specific quadrant of your angle.