linguistic:voice_change, structural:expansion
Other trigonometric functions

In addition to the six ratios listed earlier, there are additional trigonometric functions that were historically important, though seldom used today. These include the chord (crd(θ) = 2 sin(θ / 2)), the versine (versin(θ) = 1 − cos(θ) = 2 sin (θ / 2)) (which appeared in the earliest tables), the coversine (coversin(θ) = 1 − sin(θ) = versin(π / 2 − θ)), the haversine (haversin(θ) = 1 / 2 versin(θ) = sin (θ / 2)), the exsecant (exsec(θ) = sec(θ) − 1), and the excosecant (excsc(θ) = exsec(π / 2 − θ) = csc(θ) − 1). See List of trigonometric identities for more relations between these functions.