Stitz-Zeager_College_Algebra_e-book

The law of sines gives sin85 sin65 after the usual a

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Unformatted text preview: − 2 1 − 2x 2 22 √ x2 + 1 − 1 √ for x ≥ 0 1 2 x2 + 1 (l) sin arctan(x) = √ 2 x2 + 1 − 1 − √ for x < 0 2 x2 + 1 √ ∪ 2 ,1 2 14 √ π π x x 4 − x2 x + 15. If sin(θ) = for − < θ < , then θ + sin(2θ) = arcsin 2 2 2 2 2 7x x π π 1 1 1 x −2 for − < θ < , then θ − sin(2θ) = arctan 7 2 2 2 2 2 7 x + 49 √ x π x 17. If sec(θ) = for 0 < θ < , then 4 tan(θ) − 4θ = x2 − 16 − 4arcsec 4 2 4 16. If tan(θ) = 7 7 + 2kπ or x = π − arcsin + 2kπ 11 11 In [0, 2π ), x ≈ 0.6898, 2.4518 2 2 (b) x = π − arccos + 2kπ or x = π + arccos + 2kπ 9 9 In [0, 2π ), x ≈ 1.7949, 4.4883 18. (a) x = arcsin (c) x = π + arcsin(0.569) + 2kπ or x = 2π − arcsin(0.569) + 2kπ In [0, 2π ), x ≈ 3.7469, 5.6779 14 The equivalence for x = ±1 can be verified independently of the derivation of the formula, but Calculus is required to fully understand what is happening at those x values. You’ll see what we mean when you work through the details o...
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