The sin function, a fundamental trigonometric function, has several key properties essential in various mathematical and practical applications. Below are some of its most important properties:
1)Periodicity: The sin function is periodic with a period of 2π, which means it repeats its value every 2π units. This is expressed as sin(θ+2π) = sin(θ) for any angle θ.
2)Domain: The domain of the sin function is all real numbers, which means the sin function can accept any real number as an input angle. Thus, -∞ < θ < ∞.
3)Range: The range of the sin function lies between -1 and 1, which means output of the sin function is always between -1 and 1. Thus, -1 ≤ sin(θ) ≤ 1.
4)Symmetry: The sin function is an odd function, which means that sin(-θ) = -sin(θ). This symmetry implies that the graph of sin is symmetric about the origin.
5)Asymptotes: The sin 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 sin function oscillates between -1 and 1.