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Algebra IIAB Chapter 13 Test Review Algebra IIAB 1. Evaluate the 6 trigonometric functions of the angle π, exactly. a. b. 2. In a right triangle, β A and β B are acute. Give exact values. a. If tan B = 2, what is cos B? b. If tan A = 11 , 17 what is sin A? c. If sin B = 8 , 15 what is cos B? A 3. Solve the triangle at the right, with the given measurements. Round to the nearest hundredths. a. B = 45° and c = 3 C b. A = 36° and b = 8 c. A = 67° and c = 18 B d. B = 60° and a = 5 4. a. John stands 150 meters from a water tower and sights the top at an angle of elevation of 36°. If Johnβs eyes are 2 meters above the ground, how tall is the tower? Round to the nearest meter. b. John stands 250 meters from a water tower and sights the top at an angle of elevation of 28°. If Johnβs eyes are 2.6 meters above the ground, how tall is the tower? Round to the nearest meter. 5. Draw an angle with the given measure in standard position. Then find one positive coterminal angle and one negative coterminal angle. a. 58° b. 210° c. 305° e. β450° d. 580° 6. Rewrite each degree measure in radians and each radian measure in degrees. a. 18° b. β72° c. 5π 2 d. β 9π 2 7. The terminal side of ΞΈ in standard position contains each point. Find the exact values of the six trigonometric functions of ΞΈ. a. (3, 4) b. (8, β15) d. (β9, β40) c. (β4, 3) 8. Sketch each angle. Then find its reference angle.: 0° < π < 360° πππ 0 < π < 2π a. 135Λ b. 200Λ c. π£2 5π 3 9. a. Estimate the horizontal distance, given by the formula π = 32 sin 2π, traveled by a track and field long jumper who jumps at an angle of 25Λ and with an initial speed of 26 feet per second. π£2 b. Estimate the horizontal distance, given by the formula π = 32 sin 2π, traveled by a track and field long jumper who jumps at an angle of 30Λ and with an initial speed of 18 feet per second. 10. Evaluate the expression in both radians and degrees. a. cosβ1 (β β2 ) 2 1 2 b. sinβ1 (β ) c. tanβ1 (β β3 ) 3 11. Solve each equation. Round to the nearest tenth if necessary. a. cos ΞΈ = 0.05; 0Λ < π < 180Λ b. tan ΞΈ = 0.22; 0Λ < π < 180Λ d. tan ΞΈ = 10; 180Λ < π < 270Λ e. sin ΞΈ = 0.7; 90Λ < π < 180Λ 12. Find the measure of angle ΞΈ. a. 8 4.6 b. ΞΈο° ΞΈο° 3.35 c. 5 ΞΈο° 5.1 19 c. sin ΞΈ = β 0.03; 270Λ < π < 360Λ f. cos ΞΈ = β 0.5; 180Λ < π < 270Λ 13. Suppose I am riding my motorcycle, and preparing to jump a line of cars. If I drive 32 feet on a ramp before jumping, and the ramp is 8 feet high, what is the angle ΞΈ of the ramp? 14. Solve each triangle. a. d. a = 16, b = 20, C = 54° Turn over******** b. e. B = 71°, c = 6, a = 11 c. f. A = 37°, a = 20, b = 18 15. Find the area of β³ABC to the nearest tenth, if necessary. a. b. c. a = 4.86, b = 3 ft, c = 7 ft d. c = 16.4, a = 10 cm, b = 7 cm