sec2theta

Sec2theta, also known as secant squared of theta, is a trigonometric function that is defined as the square of the secant function. The secant function, sec(theta), is the reciprocal of the cosine function, cos(theta). Therefore, sec2theta can be expressed as:

sec2theta = (1 / cos(theta))^2

This function is often used in calculus and physics, particularly in the study of oscillatory motion and wave propagation. It is also a key component in the derivation of the double-angle formulas for trigonometric functions.

The domain of sec2theta is all real numbers except for values of theta where cos(theta) is zero, which occurs at theta = (2n + 1)π/2 for any integer n. At these points, sec2theta is undefined.

The range of sec2theta is all real numbers greater than or equal to 1. This is because the square of any real number is non-negative, and the minimum value of sec(theta) is 1, which occurs when theta is an integer multiple of π.

Sec2theta is an even function, meaning that sec2theta(-theta) = sec2theta(theta) for all theta in the domain. It is also periodic with a period of 2π, meaning that sec2theta(theta + 2π) = sec2theta(theta) for all theta in the domain.