Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
INTEGRATED TRIGONOMETRY FALL SEMESTER EXAM REVIEW #1 NAME_______________________________PERIOD____________DATE_____________ State the amplitude for each function. 1. y 5cos 1.____________ 2. y 2 cos 0.5 2.____________ 2 3. y sin 9 5 3.____________ State the period for each function. 4. y 3cos 2 4.____________ 5. y 6sin 3 5.____________ 6. y 2 sin 3 12 6.____________ State the phase shift for each function. 7. y 20 5cos(3 ) 7.____________ 1 8. y cos 2 4 2 8.____________ 9. y 10sin 4 5 4 9.____________ 10. What is the formula to determine the phase shift of a function? 10.____________ Looking at the graph, state the vertical shift of the function. 11. 12. 11.____________ 12.____________ Find the values of for which each equation is true. 13. 1 cos 2 14. sin 1 15. cos 0 13.____________ 14.____________ 15.____________ Find each value 16. sin 1 tan 4 2 17. sin 2 cos 1 2 18. cos(tan 1 3) 16.____________ 17.____________ 18.____________ 19. The equation d 2.7 sin(0.5m 1.4) 12.1 models the amount of daylight in Cincinnati, Ohio, for any given day. In this equation m=1 represents the middle of January, m=2 represents the middle of February etc. a. What is the least amount of daylight in Cincinnati? a.____________ b. What is the greatest amount of daylight in Cincinnati? b.____________ c. Find the number of hours of daylight in the middle of October. c.____________ 20. A buoy floats on the water bobbing up and down. The distance between its highest and lowest point is 6 centimeters. It moves from its highest point down to its lowest point and back to its highest point every 14 seconds. Write a cosine function that models the movement to the equilibrium point. 20.____________ INTEGRATED TRIGONOMETRY FALL SEMESTER EXAM REVIEW #2 NAME_______________________________PERIOD____________DATE_____________ Use the given information to determine the exact trigonometric value. 1 1. cos , 0 90 ;csc 4 2. cot 6 , ; tan 3 2 1.____________ 2.____________ Solve each equation for 0 360 . 3. 4 cos 2 x 2 0 4. sin 2 x csc x 1 0 3.____________ 4.____________ 5. 5.____________ 3 cot x 2cos x Use the given information to determine the exact trigonometric value. 2 6. cos ,90 180 ;sin 3 7. csc 11 , ;cot 3 2 6.____________ 7.____________ Use a half-angle identity to find the exact value of each function. 8. cos 15 9. sin 75 8.____________ 9.____________ 10. tan 5 12 10.____________ Use the given information to find 10. sin2 , cos2 , and tan2 . 11. cos = 12. cos = 4 , 0 90 5 sin2 ____________ 4 , 0 sin2 ____________ 5 2 cos2 ____________ tan2 ____________ cos2 ____________ tan2 ____________ INTEGRATED TRIGONOMETRY FALL SEMESTER EXAM REVIEW #3 NAME_______________________________PERIOD____________DATE_____________ Find each power. Express the result in rectangular form. 1. 3 cos i sin 6 6 3 2. 2 cos i sin 4 4 1.____________ 5 Solve each triangle. Round to the nearest tenth. 3. b 7, c 10, A 51 2.____________ 3.a=___________ B=___________ C=___________ 4. a 16, c 12, B 63 4.b=___________ A=___________ C=___________ 5. 4. C 79.3 , a 21.5, b 13 5.c=___________ A=___________ B=___________ Find the area of each triangle. Round to the nearest tenth. 6. a 4, b 6, c 8 6.____________ 7. a 17, b 13, c 19 7.____________ 8. The longest truck-mounted ladder used by the Dallas Fire Department is 108 feet long and consists of four hydraulic sections. Gerald Travis, aerial expert for the department, indicates that the optimum operating angle of this ladder is 60 . The fire fighters find they need to reach the roof of an 84-foot burning building. Assume the ladder is mounted 8 feet above the ground. a. Draw a labeled diagram of the situation. b. How far from the building should the base of the ladder be placed to achieve the optimum operating angle? 8b.____________ c. How far should the ladder be extended to reach the roof? 8c.____________ 9. When a 757 passenger jet begins its descent to the Ronald Reagan International Airport in Washington, D.C., it is 3900 feet from the ground. Its angle of descent is 6 . a. What is the plane’s ground distance to the airport? 9a.____________ b. How far must the plane fly to reach the runway? 9b.____________ Simplify the expression. 10. cos x csc x tan x 10.____________ Use the unit circle to find each value. 11.____________ 12.____________ 11. sin 90 12. tan 360 13. cot(180) 13.____________ 14. csc 270 15. cos(270) 16. sec180 14.____________ 15.____________ 16.____________ Find the values of sine, cosine, and tangent for each A . 17. B 80 A 60 C 17. Sin=____________ Cos=____________ Tan=____________ Find the values of the six trigonometric functions for angle in standard position if a point with the given coordinates lies on its terminal side. 18. ( 4, 3) 18. Sin=____________ Cos=____________ Tan=____________ Csc=____________ Sec=____________ Cot=____________ Solve each equation if 0 x 360 19. sin x 1 20. tan x 3 19.____________ 20.____________ Find each value. 21. sin 1 0 22. Arc cos 0 23. Tan 1 3 3 21.____________ 22.____________ Change each degree measure to radian measure in terms . 24. 137 25. 210 26. 300 23.____________ 24.____________ 25.____________ 26.____________ Change each radian measure to degree measure. Round to the nearest tenth. 27. 7 12 28. 11 3 29. 17 27.____________ 28.____________ 29.____________ INTEGRATED TRIGONOMETRY FALL SEMESTER EXAM REVIEW #4 NAME_______________________________PERIOD____________DATE_____________ Write each rectangular equation in polar form. 1. x 7 1.____________ Graph each polar equation. 5 2. 30 3. 4 4. 150 Express each complex number in polar form. Make sure you calculator is in degrees. 5. 6 8i 6. 4 i 7. 20 21i 5.____________ 6.____________ 7.____________ Write each polar equation in rectangular form. 8. r 3 9. r 2 10. r 2csc 8.____________ 9.____________ 10.____________ Find the polar coordinates of each point with the given rectangular coordinates. 11. (0,1) 12. (1, 3) 1 3 13. ( , ) 4 4 11.____________ 12.____________ 13.____________ Find the rectangular coordinates of each point with the given polar coordinates. 1 3 14. ( , ) 15. (1, ) 16. (2, 270 ) 14.____________ 2 4 6 15.____________ 16.____________ Simplify each expression. 17. sin x cos x sec x cot x 18. cosxtanx +sinxcotx 17.____________ 18.____________ 19. (sin x cos x)2 (sin x cos x)2 20. When do you use the law of cosines? When do you use the law of sines? 19.____________ Evaluate each function for the given value. 21. f (x ) x 2 2x find f ( 2) 21. 22. f ( x ) 2x 2 x find f ( x h ) 22. State the domain of the function, use interval notation to describe the domain. 23. f ( x) 3 x 23. 24. f ( x) 3x x 2 24. 25. f ( x) 4 x 1 25. IV. Given the following: f ( x ) 2 x 2 x 1, g ( x ) 2x 26. (f + g)(x) 26. 27. (f – g)(x) 27. 28. ( f g ) ( x ) 28. 29. ( f )( x ) g 29. 30. ( f g )( x ) 30. 31. ( g f )( x ) 31. List the transformations that change the parent function f ( x) x 2 . 32. f ( x) 1 2 x 3 33. f ( x) 32. x2 2 5 34. f ( x) (4 x) 2 V. 35. 33. 34. Determine the intervals for which the following are increasing, decreasing, or constant. Write your answers in interval notation. 36. 35. Increasing: Decreasing: Constant: 36. Increasing: Decreasing: Constant: INTEGRATED TRIGONOMETRY FALL SEMESTER EXAM REVIEW #5 NAME_______________________________PERIOD____________DATE_____________ Use the given information to determine the exact trigonometric value. 1 1. sin ,180 270 ; tan 3 1.____________ 2 3 ;cos 2. tan , 3 2 2.____________ 7 3. sec ,180 270 ;sin 5 3.____________ 4. An architect is designing a new parking garage for the city. The floors of the garage are to be 10 feet apart. The exit ramps between each pair of floors are to be 75 feet long. What is the measurement of the angle of elevation of each ramp? 5. At a certain time of day, use angle of elevation of the sun of 44. Find the length of a shadow cast by a building 30 meters high. Determine the quadrant in which the angle lies. (The angle is given in radian measure) 6. 10. _______ 5 11 _______ 9 7. 7 _______ 5 8. 11. 7 _______ 6 12. 7 ________ 4 13 ________ 4 GRAPH 2 14. f(x) sin if 2 15. f(x) cos if 4 2 16. y 4 cos 3 17. y 2sin 9. 13. _________ 12 2 _________ 3 Solve the following equations given the following stipulations. 18. Solve for 0 x 360 cos 2 x cos x 1 sin 2 x 18. 19. Solve for 0 2 cos2 3 cos 2 0 19. 20. Solve for 0 x 360 sin x cot x 21. Solve for all real values. sin x cos 2 x 1 1 2 20. 21. Write an ordered pair that represents YZ . Then find the magnitude of YZ . 22. Y 1,6 Z -2,5 23. Y 1,0 Z -3,6 22.____________ 23.____________ 24. Write LB as the sum of unit vectors. L(0,7), B(-7,-2) 24. 25. Write ST as the sum of unit vectors. S(0,4), T( 5, 4) 25. 26. Find the unit vector having the same direction as v. 26. v 5i 3 j 27. Write the vector v in the form, ai bj , given its magnitude v and the angle it makes with the positive x-axis. v 2 , 135 27.