ALGEBRAIC For the following exercises, find all solutions exactly on the ir 4. 2sin 0 = - V2 5. 2sin 0 = V3 %3D 7. 2cos 0 = –V2 8. tan 0 = -1 %D 10. cot x +1 = 0 11. 4sin? x - 2 = 0 For the following exercises, solve exactly on [0, 27). 13. 2cos 0 = V2 14. 2cos 0 = -1 16. 2sin 0 = -V3 17. 2sin(30) = 1 V3 19. 2cos(30) = -V2 20. cos(20) = %3D 22. 2cos(플e)= V3 For the following exercises, find all exact solutions on [0, 2T). 23. sec(x)sin(x) – 2sin(x) = 0 24. 25. 2cos? t + cos(t) = 1 26. 27. 2sin(x)cos(x) – sin(x) + 2cos(x) – 1 = 0 28. 29. sec? x = =D1 30. 31. 8sin?(x) + 6sin(x) + 1 = 0 32. For the following exercises, solve with the methods shown in t) 34. 33. sin(3x)cos(6x) – cos(3x)sin(6x) = -0.9 36. 35. cos(2x)cos x+ sin(2x)sin x = 1 38. 37. 9cos(20) = 9cos? 0 – 4 40. 39. cos(2t) = sin t COS %3D For the following exercises, solve exactly on the interval [0, 27T). U 42. sin? x + sin x - 2 41. tan? x – V3 tan x = 0 45. 3cos? x - 2cos x – 2 44. 5cos? x + 3cos x - 1 = 0 48. cot? x = -cot x %3D 47. tan? x + 5tan x - 1= 0 has r 27n Зл 7. 4 7ти 13. 4’4 15. 7 6. Зл 5л 11л 13л 19. 12´ 12´ 12 12 TI 5л 23. 0, –, , 25 3 3 (-) 1 31. л - sin 4 9. 33. sin-! 10 (sin (). 4 1 п- 3 35.0 37. 0= s %3D 10 1/31- 5.

Shante caught 17 ladybugs every day for 4 days. How many lady bugs does Shante need to catch on the fifth day so that she will have caught an average of 20 ladybugs per day over the 5 days? Solve this problem in two different ways, and explain you solutions.