Koszinusz

Koszinusz, also known as the cosine function, is a fundamental trigonometric function. It is defined in a right-angled triangle as the ratio of the length of the adjacent side to the length of the hypotenuse. For any angle θ, the cosine of θ, denoted as cos(θ), is represented by this ratio.

The cosine function is periodic, meaning its values repeat at regular intervals. Its domain is all real numbers, and its range is between -1 and 1, inclusive. The graph of the cosine function is a smooth, wave-like curve. It is an even function, meaning cos(-θ) = cos(θ).

In the unit circle, the cosine of an angle is represented by the x-coordinate of the point where the terminal side of the angle intersects the circle. This geometric interpretation is crucial in understanding its properties and applications.

The cosine function has numerous applications in various fields, including physics, engineering, signal processing, and mathematics. It is used to describe oscillatory phenomena, analyze waves, solve triangles, and in many areas of calculus and differential equations. The Taylor series expansion for cos(x) is 1 - x²/2! + x⁴/4! - x⁶/6! + ..., which allows for approximation of its values.