What is 1 cosx?

1/cosx is the reciprocal of the <a href="https://www.wikiwhat.page/kavramlar/cosine%20function">cosine function</a>, often written as sec x.

• Definition: 1/cosx = sec x, where sec x is called the <a href="https://www.wikiwhat.page/kavramlar/secant%20function">secant function</a>.

• Domain: The secant function is defined for all real numbers x except where cos x = 0, which occurs at x = (π/2) + nπ, where n is an integer. Therefore, the domain is all real numbers except (π/2) + nπ.

• Range: The range of sec x is (-∞, -1] ∪ [1, ∞). This is because the cosine function has a range of [-1, 1], and taking the reciprocal inverts the values.

• Period: The secant function has a period of 2π, the same as the <a href="https://www.wikiwhat.page/kavramlar/cosine%20function">cosine function</a>.

• Graph: The graph of sec x has vertical asymptotes at x = (π/2) + nπ, and it has a U-shaped curve between these asymptotes.

• Trigonometric Identities: sec x is frequently used in trigonometric identities and calculus. For example, it is used in derivatives and integrals. It also appears in Pythagorean identities: tan²x + 1 = sec²x

• Applications: The secant function is used in various applications, including physics, engineering, and navigation, particularly when dealing with angles and distances related to circles or other geometric shapes.