for all 0 ≤ α ≤ 2π

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For all 0 ≤ α ≤ 2π, trigonometric functions such as sine, cosine, and tangent are periodic with a period of 2π. This means that the values of these functions repeat every 2π radians or 360 degrees, which allows for efficient calculations and predictions in fields such as physics, engineering, and geometry.