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Assignment #1 DUE by 6/9/02 1. Find the radian measure of a central angle θ opposite an arc measure 16 inches in a circle of radius 8 inches. 2. Find the exact radian measure, in terms of π, of each angle. a. 90 b. 180 c. 270 3. Find the exact degree measure of each angle. a. b. c. 6 3 2 4. Determine which quadrant the angle d. d. 360 5 6 8 , in standard position, lies in. 3 5. Determine the radian measure for a 2/9 rotation. 6. Given triangle ABC with right angle C with opposite sides a, b, and c, respectively. Find the missing sides and angles to 3 significant digits given B = 33.7 , b = 22.4. 7. Determine whether the statement is true or false. If true, explain why. If false, give a counterexample. Let A and B be acute angles. If A < B, then cot A < cot B. 8. Explain what happens to each of the following as the acute angle θ approaches 90 : a. sin θ b. tan θ c. csc θ 9. Find the value of each of the other five trigonometric functions for an angle (without 5 finding ) given csc with being an angle in quadrant III. 4 10. Using a calculator, evaluate to 4 significant digits: cot 25.1 rad 11. Find the exact values of each of the six trigonometric functions for an angle whose terminal side is at (1, 3 ) . 12. Given cos 0 , determine the quadrants in which the terminal side of an angle must lie in. 13. Find the exact value of each of the other five trigonometric functions for an angle 2 (without finding ) given sin with angle located in quadrant III. 3 14. Use right triangle trig ratios to evaluate cot 30. Do not use a calculator or table. Leave answers involving radicals in exact radical form. 2 15. Use right triangle trig ratios to evaluate csc . Do not use a calculator or table. 3 Leave answers involving radicals in exact radical form. 16. Find the smallest positive in degree measure for which csc = -2. 17. Find exactly all , 0 θ < 360º, for which cot 1 3 . 18. Using unit circle, find the coordinates of the circular point P for x x 3 . 2 19. Find the exact values of x when cos x 1 2 , 2 x 2 . 20. Evaluate sec (45) to 4 significant digits using a calculator. 21. If sin x = -0.1377, find sin (x + 2π). and for 2