The cosine function is a fundamental mathematical function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is commonly denoted as cos and is widely used in trigonometry, physics, and engineering. The cosine function is periodic, meaning it repeats its values in regular intervals, specifically every 360 degrees or 2π radians. In the unit circle, the cosine of an angle corresponds to the x-coordinate of a point on the circle. This relationship allows for the visualization of the cosine function, which produces a wave-like graph that oscillates between -1 and 1. The cosine function is essential for analyzing periodic phenomena, such as sound waves and light waves.