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The range of arcsecant: y∈ [0; π/2)∪ ( π/2; π]. Arcsecant is a non-periodic function. The arcsecant increases and is continuous on the interval x∈ (-∞; -1] and x∈ [1, + ∞), since the secant function (x= secy) is strictly increasing and continuous in the intervals [0; π/2) and (π/2;π]
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.
Sec inverse x is also referred to by different names such as arcsec, inverse secant, and inverse sec x. The range of the trigonometric function sec x becomes the domain of sec inverse x, that is, (-∞, -1] U [1, ∞) and the range of arcsec function is [0, π/2) U (π/2, π].
It is used to determine an angle given the secant of the angle. The secant function, s e c (x), is defined as the reciprocal of the cosine function, i.e., s e c (x) = 1 c o s (x). The arcsecant function is derived from the secant function by reversing the roles of the angles and the secant ratios.
The range is the set of all valid y y values. Use the graph to find the range. Interval Notation: [0, π 2)∪(π 2,π] [0, π 2) ∪ (π 2, π] Set -Builder Notation: {y∣∣0 ≤ y ≤ π,y ≠ π 2} {y | 0 ≤ y ≤ π, y ≠ π 2}
24 wrz 2014 · The range is based on limiting the domain of the original function so that it is a one-to-one function. The graphs of the six inverse trigonometric functions are shown below. Here is an example of how to use the inverse functions: What is the exact value of sin − 1 = (√ 3 2)? This is equivalent to sin x = √ 3 2. Thus sin − 1 (√ 3 2 ...
12 sie 2024 · This section introduces the inverse trigonometric functions for cotangent, secant, and cosecant. It covers their definitions, properties, and domains, along with examples of evaluating these …
