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4-3 Part I NAME:__________________________ Review DATE:_______ Find the RATIO of the trig function indicated. Do NOT find the actual measure of the angle! 1. 2. 3. 4. Use the given point on the terminal side of the angle 𝜃 to find the trigonometric function indicated. 5. 6. 7. Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽. 8. sin 𝜃 for �2, √5� 9. csc 𝜃 for (−4, 3) 10. sec 𝜃 for �2√3, −2� Let 𝜽 be an angle in standard position. In which quadrant or quadrants can 𝜽 lie under the given conditions? 11. csc 𝜃 is negative 12. sin 𝜃 > 0 13. cos 𝜃 and sin 𝜃 have the same sign 14. cos 𝜃 is negative and tan 𝜃 is positive Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽. 12 5 𝜋 15. Given cot 𝜃 = − 5 in quadrant II. 16. Given csc 𝜃 = 4 where 2 < 𝜃 < 𝜋. Find sin 𝜃. Find tan 𝜃. 17. Given cos 𝜃 = Find sin 𝜃. √3 4 where 3𝜋 2 < 𝜃 < 2𝜋. 18. Given sec 𝜃 = − Find tan 𝜃. 15 9 where 𝜋 < 𝜃 < 3𝜋 2 . ANSWERS TO 4-3 Part I CORRECTIVE ASSIGNMENTS 1. √2 5. 9. √11 − 6 5 3 13. I and III 17. − 4 2. √13 4 7 6. − 12 10. 2√3 11. III and IV 3 12 9 65 7. −2 15. 14. III 18. 22√5 3. 3 4 =3 5 13 4. 8. 13√22 44 √5 3 12. I and II 4 16. − 3 4-3 Part II NAME:__________________________ Review DATE:_______ Find the reference angle. 1. 321° 2. 288° 3. −137° 4. 125° 5. −214° 6. −308° 7. 248° 8. 172° Find the exact value. 9. sin 30° 10. cos 60° 11. tan 135° 12. sin 150° 13. cos 225° 14. tan 150° 15. sin(−330)° 16. cos(−135) ° 17. tan(−315)° 18. csc(−270)° 19. sec 180° 20. cot 90 ° Find the exact value. 𝜋 21. sin 4 22. cos 6 25. cos 𝜋 26. tan 29. tan(− 3𝜋 4 ) 𝜋 23. tan √3 2 3𝜋 4 27. sin(− 𝜋 31. sec 2𝜋 32. cot 35. tan 𝜃 = √3 36. sin 𝜃 = 39. tan 𝜃 = −1 40. sin 𝜃 = − 2 43. csc 𝜃 = − 1 44. sec 𝜃 = undefined 4 30. csc 2 2 41. cos 𝜃 = 24. sin 3 7𝜋 If 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°, then find 𝜽 1 √2 34. cos 𝜃 = 2 33. sin 𝜃 = 37. sin 𝜃 = 0 2𝜋 38. cos 𝜃 = − 42. cot 𝜃 = 1 √2 2 5𝜋 ) 3 28. cos(− 11𝜋 6 ) 3𝜋 4 √3 2 1 45. Find all six trig functions. Fill in the table. radians 𝟓𝟓 𝟑 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 𝐭𝐭𝐭 𝜽 𝐜𝐜𝐜 𝜽 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 𝐭𝐭𝐭 𝜽 𝐜𝐜𝐜 𝜽 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 𝐭𝐭𝐭 𝜽 𝐜𝐜𝐜 𝜽 𝐬𝐬𝐬 𝜽 𝐜𝐜𝐜 𝜽 46. Find all six trig functions. Fill in the table. radians 𝝅 − 𝟒 47. Find all six trig functions. Fill in the table. radians 𝟓𝟓 𝟔 ANSWERS TO CORRECTIVE ASSIGNMENT 4-3 Part II 1. 39° 2. 72° 3. 43° 4. 55° 5. 34° 17. 1 18. 1 19. −1 20. 0 21. 9. 1 10. 2 25. −1 33. 45°, 135° 1 26. −1 37. 0°/360°, 180° 41. 30°, 330° 45. sin cos tan csc − √3 2 1 2 −√3 11. −1 2 − 2√3 3 27. − 12. √3 2 28. 34. 60°, 300° 38. 135°, 225° 42. 45°, 225° 46. sec cot sin 2 − √3 3 − √2 2 1 13. − 2 √3 2 √2 2 6. 52° √2 2 14. 22. 29. 1 √3 3 √3 2 35. 60°, 240° cos tan csc sec cot √2 2 −1 −√2 √2 −1 8. 8° 23. −√3 24. 15. 30.undefined 39. 135°, 315° 43. 270° 7. 68° 1 16. − 2 31. 1 36. 60°, 120° 47. sin 1 2 cos − √3 2 32. −1 40. 210°, 330° 44. 90°, 270° tan − √3 3 csc 2 sec − √2 2 √2 2 2√3 3 cot −√3 4-3 Part III NAME:__________________________ Review DATE:_______ EXACT VALUE = TABLE Use the table to find the EXACT value. 3𝜋 1. csc 210° 2. sin 3. cot �− 4 5𝜋 5. sin 330° 6. sin 9. csc −120° 10. cos −1260° 5𝜋 6 � 4. sec(−180°) 25𝜋 7. tan 1125° 8. cot − 11. sec −1050° 12. tan Use the table to find the angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°. √3 14. csc 𝜃 = √2 13. cos 𝜃 = − 15. sec 𝜃 = undefined 16. sin 𝜃 = 17. csc 𝜃 = −1 18. csc 𝜃 = 19. cos 𝜃 = 0 20. cot 𝜃 = √3 21. csc 𝜃 = −2 22. sec 𝜃 = − 23. tan 𝜃 = −√3 24. cot 𝜃 = 4 2 2√3 3 2√3 3 6 3𝜋 2 √2 2 √3 3 APPROXIMATE VALUE = CALCULATOR Round to the nearest hundredth! Use the calculator to find the APPROXIMATE value of each. 25. csc 70° 26. cot −115° 27. sec 140° 5𝜋 29. sin 18 𝜋 33. csc 11 7𝜋 28. sin 56° 4𝜋 30. tan − 12 31. cot 23𝜋 32. cot 34. sec −214° 35. csc 5𝜋 36. sin 4° 25 7 5 Use the calculator to find each angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°. Round to the nearest hundredth. 37. cos 𝜃 = −0.788 38. sec 𝜃 = 1.236 39. tan 𝜃 = 0.487732 40. sec 𝜃 = −1.13257 41. cot 𝜃 = −0.9004 42. csc 𝜃 = 1.28 43. sin 𝜃 = −0.35 44. tan 𝜃 = −1.81 45. csc 𝜃 = −1.92 ANSWERS TO 4-3 Part III CORRECTIVE ASSIGNMENT 1. −2 6. − 11. √2 2 2√3 3 16. 45°, 135° 21. 210°, 330° 26. 0.47 31. −3.89 36. 0.07 41. 132°, 312° √2 2 2. 7. 1 12. undefined 17. 22. 27. 32. 37. 42. 270° 150°, 210° −1.31 −1.38 142°, 218° 51.38°, 128.62° 3. √3 4. −1 13. 150°, 210° 14. 45°, 135° 8. −√3 18. 23. 28. 33. 60°, 120° 120°, 300° 0.83 3.55 9. − 2√3 3 19. 90°, 270° 24. 60°, 240° 29. 1.06 1 5. − 2 10. −1 15. 90°, 270° 20. 30°, 210° 25. 1.06 30. 3.73 35. 1.28 34. −1.21 38. 36°, 324° 39. 26°, 206° 40. 152°, 208° 43. 200.49°, 339.51° 44. 118.92°, 298.92° 45. 211.39°, 328.61°