What is the relationship between the cotangent and tangent functions?

The relationship between the cotangent and tangent functions is defined in terms of their ratios with sine and cosine. The cotangent of an angle is essentially the reciprocal of the tangent function. Tangent is defined as the ratio of the sine of the angle to the cosine of the angle, expressed mathematically as:

[ \tan(x) = \frac{\sin(x)}{\cos(x)} ]

To find the cotangent, we take the reciprocal of the tangent:

[ \cot(x) = \frac{1}{\tan(x)} ]

This relationship states that cotangent can be expressed as 1 divided by the tangent of the angle. By substituting the definition of tangent into this equation, we can further express cotangent as:

[ \cot(x) = \frac{1}{\frac{\sin(x)}{\cos(x)}} = \frac{\cos(x)}{\sin(x)} ]

This shows that cotangent relates directly to tangent through the reciprocal relationship, confirming that the statement that cotangent equals 1 divided by tangent is indeed correct.