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3 10 tan x tan x x ≠ (n + 1 2 )π ( (n − 1 2 )π, (n + 1 2 )π) (− π 2 , π 2 ) tan x Arctan x arctan x tan −1 x Arctan x R (− π 2 , π 2 ) 5 ✓ y ✏ π 2 O x − π 2 ✒ y = Arctan x 5: ✑ 3.1.1 6 (1) Arcsin 1 2 sin θ = 1 2 −π 2 ≤ θ ≤ π 2 θ Arcsin 1 2 = π 6 (2) (1) π 6 (2) − π 2 (3) π 6 (4) 3 4 π (5) π 6 (6) − π 3 3.1.2 7 (1) y 0 tan x = y 0 x tan x 0 = y 0 x 0 x = x 0 + mπ m
3 11 Arctan y 0 tan x = y 0 x − π 2 < x < π 2 tan x = y 0 x Arctan y 0 x = Arctan y 0 + mπ m f n (x) (nπ − π 2 , nπ + π 2 ) nπ − π 2 < f −1 n (y 0 ) < nπ + π 2 fn −1 (y 0 ) = x n = x 0 + nπ = Arctan y 0 + nπ y 0 fn −1 (x) = Arctan x + nπ (2) −1 ≤ y 0 ≤ 1 y 0 sin x = y 0 x sin x 0 = y 0 , − π 2 ≤ x 0 ≤ π 2 x 0 x = mπ + (−1) m x 0 m cos x = sin ( ) x + π 2 ( cos x = y 0 ⇐⇒ sin x + π ) = y 0 2 cos x ′ = y 0 x ′ x 0 x ′ = mπ + (−1) m x 0 − π 2 = 2m − 1 π + (−1) m x 0 m 2 sin x = y 0 x − π 2 ≤ x ≤ π 2 Arcsin y 0 x x ′ x = mπ + (−1) m Arcsin y 0 , x ′ = 2m − 1 π + (−1) m Arcsin y 0 2 Arcsin y 0 m nπ − π 2 ≤ g−1 n (y 0 ) ≤ nπ + π , nπ ≤ h−1 n (y 0 ) ≤ (n + 1)π n 2 gn −1 (y 0 ) x m = n h −1 n (y 0 ) x ′ m = n + 1 gn −1 (y 0 ) = nπ + (−1) n Arcsin y 0 , h −1 n (y 0 ) = 2n + 1 π + (−1) n+1 Arcsin y 0 2 y 0 [−1, 1] gn −1 (x) = (−1) n Arcsin x + nπ, h −1 n (x) = (−1) n+1 Arcsin x + 2n + 1 π 2 h −1 0 (x) = Arccos x Arccos x = − Arcsin x + π 2
Page 1 and 2: 2012 I 3 IIIII 21 24 5 24
Page 3 and 4: 2012 I 3 IIIII 21 24 5 24
Page 5 and 6: 3 3 m [a 0 , b 0 ] c, c ′ [a 0
Page 7 and 8: 3 5 x 1 < x 0 < x 2 ⇒ f(x 1 ) <
Page 9 and 10: 3 7 (f −1 ) ′ (f(x)) = 1 f
Page 11: 3 9 3.1 A ′ A A A ′ A
Page 15 and 16: 3 13 θ = Arcsin x sin (Arcsin
Page 17 and 18: 3 15 − π 2 < Arcsin x < π 2 =
Page 19 and 20: 3 17 (5) ( Arctan √ ) ′ 1
Page 21: 3 19 (5) g(h) m (1) g(h) 0 h

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