Mrs. Madden's Trigonometry class - Home



TRIGONOMETRY ReviewChapter 2 52660552120902.1 Trig Functions of Acute Angles1. Find the exact values of sine, cosine, and tangent of angle A.sinA=cosA= tanA=2. Write each function in terms of its cofunction.a. cos38.7° b. csc(θ+23°)3. Find one solution for each equation. Assume all angles involved are acute angles.a. sin4B=cos5Bb. tan5x+11°=cot(6x+2°)4. Determine whether each statement is true or false. Explain. a. sin46°<sin58° b. sec58°<csc47°5. Find the exact value of each part labeled with a variable in the figure.y49936581204302.2 Trig Functions of Non-Acute Angles6. Find the reference angle for each angle.a. 405°b. -1860° 7. Find the exact values of the six trig functions for -855°.sin-855°= csc-855°= cos-855°= sec-855°=tan-855°= cot-855°=8. Find the exact value of each expression.a. cos1215°b. tan(-1020°) 9. Find the exact value sec2300°-2cos2150°+tan45°10. Find the values of θ, if θ is in the interval [0°, 360°) and has the given function value.a. sinθ=-12 b. secθ=-22.3 Find Trig Functions Using a Calculator11. Approximate the value of each expression to the nearest ten thousandth.a. sin72°30'b. sec58.9041°12. Use a calculator to find an angle θ in the interval [0°, 90°] that satisfies the given condition. Round to the nearest hundredth.a. cosθ=.9754 b. cotθ=1.124913. The grade resistance F of an automobile traveling uphill or downhill is modeled by the equation F=Wsin θ where W is the weight of the automobile. a. What is the grade resistance of a 2100-lb car traveling on a 1.8° uphill grade? b. A 3000-lb car traveling uphill has a grade resistance of 150 lb. What is the angle of the grade?2.4 Solving Right Triangles521144511493514. Solve the right triangle.15. Solve right triangle ABC if C=90°, b=219 cm, and c=647 cm.16. A 40-ft flagpole cast a 30-foot shadow. Find the angle of elevation of the sun to the nearest degree.17. The angle of depression from a helicopter to its landing port is 64°. If the altitude of the helicopter is 1600 m, find the distance from the helicopter to the landing port to the nearest meter.2.5 Further Applications of Right Triangles18. Two ships leave a port at the same time. The first ship sails on a bearing of 32° at 16 knots (nautical miles per hour) and the second one a bearing of 122° at 24 knots. How far apart are they after 2.5 hr?19. A ship leaves a pier on a bearing of S 62° E and travels for 75 km. It then turns and continues on a bearing of N 28° E for 53 km. How far is the ship from the pier?50482503660020. Find h as indicated in the figure.21. An observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point (-4, -4). Answer Key1. sinA=4553, cosA=2853, tanA=4528 2. a. sin51.3°b. sec(67°-θ)3. a. B=10b. x=74. a. True. The larger the angle, the larger the value of sine. b. False. The larger the angle, the larger the value of secant.5. w=203, x=103, y=103, z=1066. a. θ'=45°b. θ'=60°7. sin-855°=-22 csc-855°=-2 cos-855°=-22 sec-855°=-2 tan-855°=1 cot-855°=18. a. -22b. 39. 72 or 31210. a. 210°, 330°b. 135°, 225°11. a. .9537b. 1.936212. a. 12.74°b. 41.64°13. a. 66 lbb. 2.9°14. M=38.8°, n=154 m, p=198 m15. A=70.2°, B=19.8°, a=609 cm16. 53.1°17. 1780 m18. 72 nautical miles19. 92 km20. 344 m21. 225° due north, S 45° W ................
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