cos0

Cos0 refers to the value of the cosine function at the angle zero. In standard trigonometry, cos(θ) gives the x-coordinate of a point on the unit circle corresponding to an angle θ measured from the positive x-axis. When θ = 0, the corresponding point on the unit circle is (1, 0), so cos(0) = 1. This value is the same whether the angle is expressed in radians or degrees, since zero represents the same angle in any unit.

Cosine is an even function with range [-1, 1], and cos0 = 1 represents the maximum value of the cosine function. The derivative of cos x is -sin x, which at x = 0 evaluates to 0, reflecting a horizontal tangent at that point. The Taylor series expansion around 0 starts with cos x = 1 − x^2/2! + x^4/4! − …, confirming the value at 0 is 1.

In the unit-circle interpretation, cos0 is the horizontal component of the unit vector at angle zero. The value cos0 = 1 serves as a fundamental reference point in many trigonometric identities, calculations, and applications, including physics, engineering, and Fourier analysis.