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Stitz-Zeager_College_Algebra_e-book

# To that end we let ak 2k 6k1 and bk 53 2k 6k5

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Unformatted text preview: rccos(cos(x)) = x provided 0 ≤ x ≤ π • Properties of G(x) = arcsin(x) – Domain: [−1, 1] – Range: − π , π 22 – arcsin(x) = t if and only if − π ≤ t ≤ 2 π 2 and sin(t) = x – sin(arcsin(x)) = x provided −1 ≤ x ≤ 1 – arcsin(sin(x)) = x provided − π ≤ x ≤ 2 π 2 – additionally, arcsine is odd Everything in Theorem 10.26 is a direct consequence of the facts that f (x) = cos(x) for 0 ≤ x ≤ π and F (x) = arccos(x) are inverses of each other as are g (x) = sin(x) for − π ≤ x ≤ π and 2 2 G(x) = arcsin(x). It is time for an example. 10.6 The Inverse Trigonometric Functions 703 Example 10.6.1. 1. Find the exact values of the following. (a) arccos (b) arcsin 1 2 √ (e) arccos cos (f) arccos cos 2 2 √ 11π 6 (g) cos arccos − 3 5 2 2 (c) arccos − π 6 1 (d) arcsin − 2 (h) sin arccos − 3 5 2. Rewrite the following as algebraic expressions of x and state the domain on which the equivalence is valid. (a) tan (arccos (x)) (b) cos (2 arcsin(x)) Solution. 1. (a) To ﬁnd arccos 1 , we need to ﬁnd th...
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