Answer: These exercises use results from plane geometry to obtain exact values of the

Chapter 5, Problem 83

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These exercises use results from plane geometry to obtain exact values of the trigonometric functions of 15. Start with a right triangle ACB having a 60 angle at A and a 30 angle at B. Let the hypotenuse of this triangle have length 2. Extend side BC and draw a semicircle with diameter along BC extended, center at B, and radius AB. Draw segment AE. (See the figure.) Any angle inscribed in a semicircle is a right angle, so triangle EAD is a right triangle. Work Exercises 7784 in order. Show that AE has length 26 - 22 and find sin 15.

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