Stitz-Zeager_College_Algebra_e-book

For our rst case consider the triangle abc below all

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Unformatted text preview: triangle (with ∠BAD being the right angle) by showing that the sides of the triangle satisfy the Pythagorean Theorem. (b) Use AOB to show that α = arctan(1) (c) Use B AD to show that β = arctan(2) (d) Use B CD to show that γ = arctan(3) (e) Use the fact that O, B and C all lie on the x-axis to conclude that α + β + γ = π . Thus arctan(1) + arctan(2) + arctan(3) = π . 10.6 The Inverse Trigonometric Functions 10.6.6 725 Answers π 1. (a) arcsin (−1) = − 2 √ π 3 (b) arcsin − =− 2 3 √ 2 π (c) arcsin − =− 2 4 π 1 =− 2 6 (e) arcsin (0) = 0 (f) arcsin (g) arcsin (h) arcsin (d) arcsin − 2. (a) arccos (−1) = π √ 3 = (b) arccos − 2 √ 2 (c) arccos − = 2 (d) arccos − 1 2 (e) arccos (0) = = 5π 6 2π 3 π 2 √ π 3. (a) arctan − 3 = − 3 π (b) arctan (−1) = − 4 √ 3 π (c) arctan − =− 3 6 (d) arctan (0) = 0 √ 5π 4. (a) arccot − 3 = 6 3π (b) arccot (−1) = 4 √ 3 2π (c) arccot − = 3 3 π (d) arccot (0) = 2 π 5. (a) arcsec (2) = 3 π (b) arccsc (2) = 6 √ 3 2 (i) arcsin (1) = (f) arccos 3π 4 1 π...
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