Stitz-Zeager_College_Algebra_e-book

54 and 1055 using extended interval notation we will

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Unformatted text preview: , cosecant and cotangent functions as presented in Theorem 10.11. 13. As we did in Exercise 8 in Section 10.2, let α and β be the two acute angles of a right triangle. (Thus α and β are complementary angles.) Show that sec(α) = csc(β ) and tan(α) = cot(β ). The fact that co-functions of complementary angles are equal in this case is not an accident and a more general result will be given in Section 10.4. 9 You may need to review Sections 2.2 and 6.2 before attacking the next two problems. 652 Foundations of Trigonometry π sin(θ) < 1 for 0 < θ < . Use the diagram from 14. We wish to establish the inequality cos(θ) < θ 2 the beginning of the section, partially reproduced below, to answer the following. y Q 1 P θ O (a) Show that triangle OP B has area B (1, 0) x 1 sin(θ). 2 (b) Show that the circular sector OP B with central angle θ has area (c) Show that triangle OQB has area 1 tan(θ). 2 (d) Comparing areas, show that sin(θ) < θ < tan(θ) for 0 < θ < 1 θ. 2 π . 2 sin(θ) π < 1 for 0 < θ < . θ 2 π sin(θ) for 0 < θ < . Combine th...
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