Stitz-Zeager_College_Algebra_e-book

85 30 c 525 units 5 30 a 3 units c

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Unformatted text preview: ) 7π 6 (d) arcsec (−1) = π √ 5π (b) arccsc − 2 = 4 2π 8. (a) arcsec (−2) = 3 √ 3π (b) arcsec − 2 = 4 π 9. (a) arccsc (−2) = − 6 (b) = 4 5 (j) csc arccos − (k) sin arcsin 3 5 (o) cos 1 arcsin 2 5 13 3 7 = 13 12 =− 5 12 1 arctan 2 (n) tan arcsin − π 2 − arctan − (l) cos 2 arccos (m) sin π 3 4 5 = (p) sin 2 arccos − 24 25 = = 117 125 31 49 + arccos 28 53 24 7 1 26 12 13 49 53 =− 336 625 =− 33 56 10.6 The Inverse Trigonometric Functions 727 11. (a) sin (arccos (x)) = for −1 ≤ x ≤ 1 √ 1 − x2 1 for all x 1 + x2 x (c) tan (arcsin (x)) = √ 1 − x2 for −1 < x < 1 √ (d) sec (arctan (x)) = 1 + x2 for all x (b) cos (arctan (x)) = √ (e) csc (arccos (x)) = √ for −1 < x < 1 1 1 − x2 2x for all x +1 √ (g) sin (2 arccos (x)) = 2x 1 − x2 for −1 ≤ x ≤ 1 1 − x2 (h) cos (2 arctan (x)) = for all x 1 + x2 (f) sin (2 arctan (x)) = x2 (i) sin (arcsin(x) + arccos(x)) = 1 for −1 ≤ x ≤ 1 √ 1 − x2 − x2 √ for −1 ≤ x ≤ 1 (j) cos (arcsin(x) + arctan(x)) = 1 + x2 √ √ √√ 2x 1 − x2 2 22 (k) tan (2 arcsin(x)) = for x in −1, − ,...
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