Pi
Units of angle

The trigonometric functions rely on angles, and mathematicians generally use radians as units of measurement. π plays an important role in angles measured in radians, which are defined so that a complete circle spans an angle of 2 π radians. The angle measure of 180° is equal to π radians, and 1° = π /180 radians.

Common trigonometric functions have periods that are multiples of π; for example, sine and cosine have period 2 π, so for any angle θ and any integer k, sin θ = sin (θ + 2 π k) and cos θ = cos (θ + 2 π k). {\displaystyle \sin \theta =\sin \left(\theta +2\pi k\right){\text{ and }}\cos \theta =\cos \left(\theta +2\pi k\right).}
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