College Trigonometry, 2011a

10.6 The Inverse Trigonometric Functions 831
Theorem 10.29. Properties of the Arcsecant and Arccosecant Functions a
ˆ Properties of F (x) = arcsec(x)
– Domain: {x : |x| ≥1} =(−∞, −1] ∪ [1, ∞)
– Range: [ 0, π ) [ )
2 ∪ π,
3π
2
– as x →−∞, arcsec(x) → 3π −
2 ;asx →∞, arcsec(x) →
π −
2
– arcsec(x) =t ifandonlyif0≤ t< π 2 or π ≤ t< 3π 2
and sec(t) =x
– arcsec(x) = arccos ( )
1
x for x ≥ 1only
b
– sec (arcsec(x)) = x provided |x| ≥1
– arcsec(sec(x)) = x provided 0 ≤ x< π 2 or π ≤ x< 3π 2
ˆ Properties of G(x) = arccsc(x)
– Domain: {x : |x| ≥1} =(−∞, −1] ∪ [1, ∞)
– Range: ( 0, π ] ( ]
2 ∪ π,
3π
2
– as x →−∞, arccsc(x) → π + ;asx →∞, arccsc(x) → 0 +
– arccsc(x) =t ifandonlyif0