What Is the Period of the Function f(x) = cos(x)?

The period of f(x) = cos(x) is 2π (or 360°).

A function's period is the smallest positive value T such that f(x + T) = f(x) for all x.

For the cosine function:

• cos(x + 2π) = cos(x) for all x
• The wave pattern repeats every 2π radians
• In degrees: completes one full cycle every 360°

Visual Understanding: Starting from any point on the cosine curve, traveling 2π units horizontally brings you back to the same y-value, and the pattern begins repeating identically.

Key Takeaways:

• Standard period: 2π radians or 360°
• Fundamental trigonometric period
• Modified by coefficients: f(x) = cos(bx) has period 2π/|b|