sec2phi

sec2phi is a mathematical expression representing the square of the secant of an angle phi. The secant function, denoted as sec(phi), is defined as the reciprocal of the cosine function, i.e., sec(phi) = 1 / cos(phi). Therefore, sec2phi is equivalent to (1 / cos(phi))^2, which simplifies to 1 / cos^2(phi).

This expression is frequently encountered in trigonometry and calculus, particularly in integration and differentiation problems involving trigonometric functions. For instance, the derivative of the tangent function, tan(phi), is sec^2(phi). This relationship is fundamental in many calculus identities.

The value of sec2phi is always greater than or equal to 1, as the cosine function's absolute value is at most 1. When cos(phi) is 1 or -1, sec(phi) is 1 or -1 respectively, leading to sec^2(phi) being 1. As cos(phi) approaches 0, sec(phi) approaches infinity, and consequently, sec^2(phi) also approaches infinity. The function is undefined when cos(phi) = 0, which occurs at phi = pi/2 + n*pi, where n is an integer.