Search results
For sin/cos/tan/cot, there is a widely accepted range. However, for sec/cosec, there are two different conventions. You can check wikipedia for more details. "one-to-one" by itself just means injective. but "a one-to-one correspondence" is bijective, or "a bijection"
Arcsine's range comes from restricting sine's domain to $[-\pi/2,\ \pi/2]$ which covers the whole range of $[-1,1]$ and also includes the origin. Arcsecant's range comes from the arccosine's range. To make cosine invertible, the domain is restricted to $[0,\pi]$.
Wikipedia says "Some authors define the range of arcsecant to be ($0 \le y < \pi/2$ or $\pi \le y < 3\pi/2$), because the tangent function is nonnegative on this domain." It is likely that your course adheres to this convention (and you are requested to comply).
For a similar reason, the same authors define the range of arccosecant to be ( - π < y ≤ - π /2 or 0 < y ≤ π /2 ).) If x is allowed to be a complex number , then the range of y applies only to its real part. Trigonometric functions of inverse trigonometric functions are tabulated below.
26 lis 2024 · About MathWorld; MathWorld Classroom; Contribute; MathWorld Book; wolfram.com; 13,209 Entries; Last Updated: Tue Nov 26 2024 ©1999–2024 Wolfram Research, Inc.
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains.
