koszinuszfüggvénynek

The cosine function, often denoted as cos(x), is a fundamental trigonometric function. It is one of the six standard trigonometric functions and is defined in the context of a right-angled triangle as the ratio of the length of the adjacent side to the length of the hypotenuse. For an angle θ in a right-angled triangle, cos(θ) = adjacent/hypotenuse.

Beyond its geometric interpretation, the cosine function can be understood through the unit circle. On the unit circle, where the radius is 1, the cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the circle. The cosine function is periodic with a period of 2π, meaning that cos(x + 2π) = cos(x) for all values of x.

The domain of the cosine function is all real numbers, and its range is the closed interval [-1, 1]. The graph of the cosine function is a wave-like curve that oscillates between -1 and 1. Key points on the graph include cos(0) = 1, cos(π/2) = 0, cos(π) = -1, and cos(3π/2) = 0.

The cosine function has numerous applications in various fields, including physics (e.g., describing simple harmonic motion, wave phenomena), engineering (e.g., signal processing, electrical engineering), mathematics (e.g., calculus, Fourier analysis), and computer graphics. Its relationship with the sine function is given by the identity cos^2(x) + sin^2(x) = 1, and it can be expressed as a Taylor series: cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...