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Math 120 Notes 8.3 – Special Values of the Trig Functions I. Special Triangles A. B. C. Evaluate the 6 trig functions at each of the following angles. 1. 4 2. 6 3. 3 Evaluate the following without using a calculator. 1. 4 cos 45 2 sin 45 2. 1 tan2 30 csc2 45 3. cot Use the calculator to evaluate the following. Round to three decimal places. 1. II. cos 4 6 cos 28 2. cot 14 Application A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at and angle as shown in the diagram. (a) Express the area A of the opening as a function of . (b) Find the area of the opening for = 30°, = 45°, = 60°, and = 75° (use the calculator only for the last computation). (c) Graph your area formula from (a). Find the angle that makes the largest area. Thus, you will find the bending angle that will allow the most water to flow through the gutter.