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Inverse Trigonometric Functions

Question 2 • IC Pre-Cal - Deering

The graph shows y = cot(x). Which of the following are true of its inverse? Check all that apply.

Answer
A
Zeros: None
B
Domain: All real numbers
C
Range: [0, π]
D
Minimum: 0
E
Maximum: None
F
Increasing intervals: The entirety of its domain

Explanation

The inverse cotangent is conventionally defined with range (0, π), so it never equals 0 and has neither a minimum nor a maximum. Its domain is all real numbers, since cotangent takes every real value on its standard one-to-one interval. It is decreasing, not increasing; and the range is not [0, π] because 0 and π are excluded.

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