Final answer:
The domain, intercepts, and some asymptotes are the same for both the tangent and cotangent functions.
Step-by-step explanation:
The tangent and cotangent functions are both trigonometric functions that relate to the sides of a right triangle. They have different ranges, asymptotes, and periods, but they share the same domain, intercepts, and some asymptotes.
The domain of both the tangent and cotangent functions is the set of all real numbers except for the values where the functions are undefined, which occur when the cosine function is equal to zero. In other words, the tangent and cotangent functions are undefined at odd multiples of π/2.
The tangent function has a range of all real numbers, while the cotangent function has a range of all real numbers excluding 0. This means that tangent can take any value, positive or negative, whereas cotangent can take any non-zero real value.
Both the tangent and cotangent functions have intercepts at the points where their graphs cross the x-axis, which occur at multiples of π for tangent and π/2 for cotangent.
The period of the tangent function is π, meaning that it repeats every π units. The cotangent function, on the other hand, has a period of π, meaning it repeats every π units as well.
Lastly, the tangent function has vertical asymptotes at odd multiples of π/2, while the cotangent function has vertical asymptotes at even multiples of π/2.