The cos function, is a fundamental trigonometric function, has several key properties that are essential in various mathematical and practical applications. Below are some of its most important properties:
1)Periodicity: The cos function is periodic with a period of 2π, which means it repeats its value every 2π units. This is expressed as cos(θ+2π) = cos(θ) for any angle θ.
2)Domain: The domain of the cos function is all real numbers, which means the cos function can accept any real number as an input angle. Thus, -∞ < θ < ∞.
3)Range: The range of the cos function lies between -1 and 1, which means output of the cos function is always between -1 and 1. Thus, -1 ≤ cos(θ) ≤ 1.
4)Symmetry: The cos function is an even function, which means that cos(-θ) = cos(θ). This symmetry implies that the graph of cos is symmetric about the y-axis.
5)Asymptotes: The cos function does not have vertical asymptotes because it is defined for all real values of θ. It also does not have horizontal asymptotes because the cos function oscillates between -1 and 1.