Math Quiz 5 Review Answer Key

Advanced Math Review 5.1-5.2 Quiz Find the measure of the complement and supplement (if possible) for each angle. 𝜋 6 2𝜋 3 1. 112° 2. 25° 3. 1. Comp.:_______ 2. Comp.:_______ 3. Comp.:_______ 4. Comp.:_______ 1. Supp.:_______ 2. Supp.:_______ 3. Supp.:_______ 4. Supp.:_______ 4. Determine the measure of the positive angle with measure less than 𝟑𝟔𝟎° that is coterminal with the given angle. Then classify the angle by quadrant. Assume the angles are in standard position. 5. 790° 6. 1123° 7. −900° 8. −1052° 5. Coterminal:_______ 6. Coterminal:_______ 7. Coterminal:_______ 8. Coterminal:_______ 5. Quadrant:_______ 6. Quadrant:_______ 7. Quadrant:_______ 8. Quadrant:_______ ~What is the formula to convert from degrees to radians? Convert the degree measure to exact radian measure. 9. 45° 10. −120° 11. −210° 12. 315° 9. Radians:_______ 10. Radians:_______ 11. Radians:_______ 12. Radians:_______ ~What is the formula to convert from radians to degrees? Convert the radian measure to exact degree measure. 13. 2𝜋 5 13. Degrees:_______ 14. – 3𝜋 4 14. Degrees:_______ 15. – 2𝜋 9 15. Degrees:_______ 16. 7𝜋 12 16. Degrees:_______ Use your calculator to convert the degree measure to radian measure. Round your answers to the nearest hundredth. 17. 72° 18. −103° 17. Radians:_______ 18. Radians:_______ Use your calculator to convert the radian measure to degree measure. Round your answers to the nearest hundredth. 19. 2𝜋 7 20. 10.25 19. Degrees:_______ 20. Degrees:_______ ~What is the formula to find arc length? Find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round approximate answers to the nearest hundredth. 21. 𝑟 = 4 inches, 𝑠 = 15 inches 21. 𝜃 = _________ 22. 𝑟 = 3.2 meters, 𝑠 = 5.8 meters 22. 𝜃 = _________ Find the length of the arc that subtends a central angle with the given measure in a circle with the given radius. Round answers to the nearest hundredth. 23. 𝑟 = 6 yards, 𝜃= 𝜋 5 23. 𝑠 = _________ 24. 𝑟 = 7.2 feet, 𝜃= 4𝜋 9 24. 𝑠 = _________ ~What is the formula to find the area of a sector? Find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle. 25. 𝑟 = 7 mm, 𝜃= 25. 𝐴 = _________ 𝜋 3 radians 26. 𝑟 = 30 cm, 𝜃 = 0.75 radians 26. 𝐴 = _________ 27. Find the values of the six trig functions of 𝜃 for the right triangle given. Reduce all ratios when appropriate. 𝐬𝐢𝐧 𝜽 = 𝐜𝐬𝐜 𝜽 = 𝐜𝐨𝐬 𝜽 = 𝐬𝐞𝐜 𝜽 = 𝐭𝐚𝐧 𝜽 = 𝐜𝐨𝐭 𝜽 = 𝜃 10 6 28. Find the values of the six trig functions of 𝜃 for the right triangle given. Reduce all ratios when appropriate. 𝐬𝐢𝐧 𝜽 = 𝐜𝐬𝐜 𝜽 = 𝐜𝐨𝐬 𝜽 = 𝐬𝐞𝐜 𝜽 = 𝐭𝐚𝐧 𝜽 = 𝐜𝐨𝐭 𝜽 = 𝜃 3 5 29. Let 𝜃 be an acute angle of a right triangle for which sin 𝜃 = 7 . 25 Find the other five trig functions. Draw a triangle first and label all the sides! 𝐬𝐢𝐧 𝜽 = 𝐜𝐬𝐜 𝜽 = 𝐜𝐨𝐬 𝜽 = 𝐬𝐞𝐜 𝜽 = 𝐭𝐚𝐧 𝜽 = 𝐜𝐨𝐭 𝜽 = 2 30. Let 𝜃 be an acute angle of a right triangle for which tan 𝜃 = 7. Find the other five trig functions. Draw a triangle first and label all the sides! 𝐬𝐢𝐧 𝜽 = 𝐜𝐬𝐜 𝜽 = 𝐜𝐨𝐬 𝜽 = 𝐬𝐞𝐜 𝜽 = 𝐭𝐚𝐧 𝜽 = 𝐜𝐨𝐭 𝜽 = ~Label the sides of this 𝟑𝟎° − 𝟔𝟎° − 𝟗𝟎° triangle 60° 30° ~Label the sides of this 𝟒𝟓° − 𝟒𝟓° − 𝟗𝟎° triangle. 45° 45° 𝐬𝐢𝐧 𝟑𝟎° = 𝐜𝐬𝐜 𝟑𝟎° = 𝐬𝐢𝐧 𝟔𝟎° = 𝐜𝐬𝐜 𝟔𝟎° = 𝐜𝐨𝐬 𝟑𝟎° = 𝐬𝐞𝐜 𝟑𝟎° = 𝐜𝐨𝐬 𝟔𝟎° = 𝐬𝐞𝐜 𝟔𝟎° = 𝐭𝐚𝐧 𝟑𝟎° = 𝐜𝐨𝐭 𝟑𝟎° = 𝐭𝐚𝐧 𝟔𝟎° = 𝐜𝐨𝐭 𝟔𝟎° = 𝐬𝐢𝐧 𝟒𝟓° = 𝐜𝐬𝐜 𝟒𝟓° = 𝐜𝐨𝐬 𝟒𝟓° = 𝐬𝐞𝐜 𝟒𝟓° = 𝐭𝐚𝐧 𝟒𝟓° = 𝐜𝐨𝐭 𝟒𝟓° = Make sure to complete the diagrams & tables above BEFORE attempting #31-34. 31. Find sin 60° + cos 30° 31.)_______________________ 32. Find csc 30° + sin 60° 32.)_______________________ 𝜋 𝜋 33. Find sin 6 − cos 3 34. Find sin 𝜋 6 cos 33.)_______________________ 𝜋 3 34.)_______________________ 35. Use your calculator to find the value of the trigonometric function to four decimal places (nearest ten thousandth). Don’t forget to check the mode of your calculator before doing these!! a. cos 𝜋 8 b. sec 𝜋 10 35a.)______________________ 35b.)______________________ c. cot 216° d. csc 114.75° 35c.)______________________ 35d.)______________________ Round answers to the nearest tenth. 36. A rocket is fired in the air at an angle of elevation of 62°. When the rocket is a ground distance of 1.5 miles away, what is its height? 36.)________________ 37. From a point 230 meters from the base of an apple tree, the angle of elevation to the top of the tree is 59.6°. Find the height of the tree to the nearest meter. 37.)________________ 38. A 50-foot ladder is leaning against a building. The angle of elevation of the ladder to the top of the building is 14.8°. How far away is the ladder from the base of the building? 38.)________________ 39. A 65-foot ladder is leaning against a house. The angle the ladder makes with the building is 52.3°. How far away is the base of the ladder from the house? 39.)________________ 40. An airplane is flying at an altitude of 15,000 feet. The pilot spots the far end of the runway at an angle of depression of 38°. What is the ground distance to the far end of the runway? 40.)________________ 41. Two children are playing up in a tree house that is 25 feet off the ground. There is a special slide they can use to exit the tree house. They see the slide at an angle of depression of 20°. How long is the slide? 41.)________________ Solve for the indicated sides. 42. AB = _____ AC = ______ 43. AC = _____ BC = ______ 44. PM = _____ MN = _____ 45. DE = 22, ∠𝐶 = 90°, ∠𝐷 = 30° Find: CD=____EC = ____ ∠𝐸 =___ B B P 7√2 5 12 N C A C M A Answers: 𝜋 3 5𝜋 6 𝜋 3 1. Comp.: None; Supp: 68° 2. Comp: 65°; Supp: 155° 3. Comp: 5. Cot. : 70° ; Quad.: 1 6. Cot. : 43° ; Quad.: 1 7. Cot.: 180° ; Quad.: None, on the axis: quadrantal 8. Cot. : 28° ; Quad.: 1 9. 14. −135° 16. 105° 15. −40° 21. 3.75 radians 𝜋 4 10. − 2𝜋 3 17. 1.26 22. 1.8125 radians 11. − ; Supp: 7𝜋 6 18. −1.80 26. 337.5 cm2 27. cos 𝜃 = tan 𝜃 = 5√34 34 3√34 cos 𝜃 = 34 5 tan 𝜃 = 3 sin 𝜃 = 28. √34 5 √34 sec 𝜃 = 3 3 cot 𝜃 = 5 csc 𝜃 = 4 + √3 7 25 24 25 7 24 sin 𝜃 = 29. cos 𝜃 = tan 𝜃 = 33. 0 7𝜋 4 13. 72° 19. 51.43° 23. 3.77 yards sin 𝜃 = 25. 25.66 mm2 12. 4. Comp: None; Supp: csc 𝜃 = sec 𝜃 = cot 𝜃 = 25 7 25 24 24 7 4 5 3 5 4 3 20. 587.28° 24. 10.05 feet csc 𝜃 = sec 𝜃 = cot 𝜃 = 5 4 5 3 3 4 2√53 53 7√53 cos 𝜃 = 53 2 tan 𝜃 = 7 sin 𝜃 = 30. √53 2 √53 sec 𝜃 = 7 7 cot 𝜃 = 2 csc 𝜃 = 1 31. √3 32. 35a. 0.9239 35b. 1.0515 36. 2.82 mi 37. 392 m 38. 48.34 ft 39. 51.43 ft 40. 19,199.12 ft 41. 73.10 ft 42. 12√2 ; 12 43. 7; 7 44. 10; 5√3 45. 11√3; 11; 60° 2 34. 4 35c. 1.3764 35d. 1.1011