cossenos

Cossenos, in trigonometry, refer to the cosine function, commonly written as cos x. They can be defined in several equivalent ways: as the ratio of the adjacent side to the hypotenuse in a right triangle, as the x-coordinate of a point on the unit circle corresponding to an angle x, or via the complex exponential formula cos x = (e^(ix) + e^(−ix))/2. The cosine function is defined for all real numbers and extends to complex arguments as well.

Key properties include that cossenos form an even, 2π-periodic function with range [−1, 1]. They satisfy the Pythagorean identity cos^2 x + sin^2 x = 1, with sin x as the corresponding sine function. Cosine is related to sine by cofunctions and phase shifts: cos(x) = sin(π/2 − x) and cos(x ± y) = cos x cos y ∓ sin x sin y. The derivative is −sin x, and the integral is sin x + C. Special values at common angles (for example cos 0 = 1, cos π/2 = 0, cos π = −1) are frequently used in calculations. The unit circle provides a geometric interpretation: the cosine of an angle is the horizontal coordinate of the point on the circle.

Cossenos have wide applications in physics, engineering, computer graphics, and signal processing. They underpin harmonic analysis, Fourier transforms, and numerous numerical methods. They are often evaluated via series expansions, such as cos x = sum_{n=0}^∞ (−1)^n x^{2n}/(2n)!, or through their relationship with complex exponentials for efficient computation.