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Properties of Cosine Function

Definition: For any angle x (in radians or degrees), cos(x) gives the x-coordinate of the point on the unit circle for that angle.

Domain: All real numbers (from minus infinity to plus infinity).

Range: From -1 to 1.

Periodicity: cos(x) repeats its values every 2pi radians (360 degrees).

Even Function: cos(-x) = cos(x), meaning its graph is symmetric about the y-axis.

Zeros: cos(x) = 0 when x = pi/2 + n*pi, where n is any integer.

Maximum Value: 1, occurring at x = 2n*pi.

Minimum Value: -1, occurring at x = pi + 2n*pi.

Increasing Intervals: From pi to 2pi (and repeats every 2pi).

Decreasing Intervals: From 0 to pi (and repeats every 2pi).

Derivative: The derivative of cos(x) is -sin(x).

Integral: The integral of cos(x) is sin(x) + C.
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