Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: tain g −1 (x) = arccot(x). Once again, the vertical asymptotes x = 0 and x = π of the graph of g (x) = cot(x) become the horizontal asymptotes y = 0 and y = π in the graph of g −1 (x) = arccot(x). y y π 1 π 4 π 2 3π 4 π 3π 4 x π 2 −1 π 4 −1 1 reflect across y = x −− − − − −→ −−−−−− g (x) = cot(x), 0 < x < π . switch x and y coordinates g −1 (x) = arccot(x). x 706 Foundations of Trigonometry Theorem 10.27. Properties of the Arctangent and Arcotangent Functions • Properties of F (x) = arctan(x) – Domain: (−∞, ∞) – Range: − π , π 22 – as x → −∞, arctan(x) → − π + ; as x → ∞, arctan(x) → 2 – arctan(x) = t if and only if − π < t < 2 – arctan(x) = arccot 1 x π 2 π− 2 and tan(t) = x for x > 0 – tan (arctan(x)) = x for all real numbers x – arctan(tan(x)) = x provided − π < x < 2 π 2 – additionally, arctangent is odd • Properties of G(x) = arccot(x) – Domain: (−∞, ∞) – Range: (0, π ) – as x → −∞, arccot(x) → π − ; as x → ∞, arccot(x) → 0+ – arccot(x) = t if and only if 0 < t < π and cot(t) = x – arccot(x) = arctan 1 x for x > 0 – cot (arccot(x)...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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