11X1 T04 02 angles of any magnitude (2011)

Download 11X1 T04 02 angles of any magnitude (2011)

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1. Angles of Any Magnitude 2. Angles of Any Magnitudey 90 III180 0 x 360III IV270 3. Angles of Any Magnitudey 90 III180 0 x 360III IV270 4. Angles of Any Magnitudey 90 III180 0x 360III IV270 5. Angles of Any Magnitudey 90 III180 0x 360III IV270 Quadrant I - normal 6. Angles of Any Magnitudey 90 III180 0 x 360III IV270 Quadrant I - normal Quadrant II - 180 sin cos tan 7. Angles of Any Magnitudey 90 III180 0 x 360III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 sin sin cos cos tan tan 8. Angles of Any Magnitudey 90 III180 0 x 360III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 9. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 III 0.9848180 0 x 360III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 10. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 ii tan 220 tan 40 III 0.9848 0.8391180 0 x 360III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 11. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 ii tan 220 tan 40 III 0.9848 0.8391180 0 iii sec105 sec 75 x 360 3.8637III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 12. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 ii tan 220 tan 40 III 0.9848 0.8391180 0 iii sec105 sec 75 iv cos 430 cos 70 x 360 3.8637 0.3420III IV270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 13. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 ii tan 220 tan 40 III 0.9848 0.8391180 0 iii sec105 sec 75 iv cos 430 cos 70 x 360 3.8637 0.3420III IV v tan 67 tan 293270 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 14. Angles of Any Magnitudey 90e.g. i sin 260 sin 80 ii tan 220 tan 40 III 0.9848 0.8391180 0 iii sec105 sec 75 iv cos 430 cos 70 x 360 3.8637 0.3420III IV v tan 67 tan 293 tan 67270 2.3559 Quadrant I - normal Quadrant II - 180 Quadrant III - 180 Quadrant IV - 360 sin sin sin cos cos cos tan tan tan 15. (vi) Find the coordinates of P y P 30 5 x 16. (vi) Find the coordinates of Px cos30 y5 P 30 5 x 17. (vi) Find the coordinates of Px cos30 y5 x 5cos30 P 30 5 3 5 xx2 18. (vi) Find the coordinates of Pxy cos30 sin 30 y55 x 5cos30 P 30 5 3 5 xx2 19. (vi) Find the coordinates of Pxy cos30 sin 30y55 x 5cos30y 5sin 30 P 30 5 3 5 5 xxy22 5 3 5 P , 2 2 20. (vi) Find the coordinates of P xy cos30 sin 30y 55x 5cos30 y 5sin 30 P305 3 5 5 x xy 225 3 5P , 2 2Boundary Values y 90180 0x 270 21. (vi) Find the coordinates of P xy cos30 sin 30 y 55x 5cos30 y 5sin 30P 305 3 55 x xy 225 3 5P , 2 2Boundary Values90 1 y0 900180 0 1x 270 22. (vi) Find the coordinates of P xy cos30 sin 30y 55x 5cos30 y 5sin 30 P305 3 5 5 x xy 225 3 5P , 2 2Boundary Values901 y0 90 0180 001x sin 0 0 270 cos 0 1tan 0 0 23. (vi) Find the coordinates of P xy cos30 sin 30 y 55x 5cos30 y 5sin 30P 305 3 55 x xy 225 3 5P , 2 2Boundary Values90 1 y0 90 0180 00 1 90x sin 0 0 sin 90 1 270 cos 0 1 cos90 0tan 0 0 tan 90 1 0 undefined 24. (vi) Find the coordinates of P xy cos30 sin 30 y 55x 5cos30 y 5sin 30P 305 3 55 x xy 225 3 5P , 2 2Boundary Values90 1 y0 90 0180 00 1 90 180x sin 0 0 sin 90 1 sin180 0 270 cos 0 1 cos90 0cos180 1tan 0 0 tan 90 1 tan180 0 0 undefined 25. (vi) Find the coordinates of P xy cos30 sin 30 y 55x 5cos30 y 5sin 30P 305 3 55 x xy 225 3 5P , 2 2Boundary Values90 1 y0 90 0180 00 1 90 180270x sin 0 0 sin 90 1 sin180 0sin 270 1 270 cos 0 1 cos90 0cos180 1 cos 270 0tan 0 0 tan 90 1 tan180 0 tan 270 1 0 0 undefinedundefined 26. Trigonometric Graphs 27. Trigonometric Graphs plot boundary values 28. Trigonometric Graphs plot boundary valuesy360 180 180 360540 720 x -1 29. Trigonometric Graphs plot boundary valuesy1360 180 180 360540 720 x -1 30. Trigonometric Graphs plot boundary valuesy1360 180 180 360540 720 x -1 31. Trigonometric Graphs plot boundary valuesy1360 180 180 360540 720 x -1 32. Trigonometric Graphs plot boundary valuesy1 y sin x360 180 180360 540720 x -1domain : all real x range : - 1 y 1 period: 360 33. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real xodd function range : - 1 y 1 sin x sin x period: 360 34. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real xodd function range : - 1 y 1 sin x sin x y period: 360 1360 180 180 360540 720 x -1 35. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real xodd function range : - 1 y 1 sin x sin x y period: 360 1360 180 180 360540 720 x -1 36. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real xodd function range : - 1 y 1 sin x sin x y period: 360 1360 180 180 360540 720 x -1 37. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real x odd function range : - 1 y 1 sin x sin x y period: 360 1y cos x360 180 180 360540 720 x -1 38. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real x odd function range : - 1 y 1 sin x sin x y period: 360 1y cos x360 180 180 360540 720 x -1 domain : all real x range : - 1 y 1period: 360 39. Trigonometric Graphs plot boundary valuesy1y sin x360 180 180 360540 720 x -1domain : all real x odd function range : - 1 y 1 sin x sin x y period: 360 1y cos x360 180 180 360540 720 x -1 domain : all real xeven function range : - 1 y 1 cos x cos xperiod: 360 40. y360 180 180 360 540 720 x 41. y360 180 180 360 540 720 x 42. y y tan x360 180 180 360 540 720 x 43. y y tan x360 180 180 360 540 720 x 44. yy tan x360 180180 360 540 720 x domain: all real x except x 90 180k , where k is an integer range: all real yperiod: 180 45. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 tan x tan x 46. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1360 180180 360 x-1 47. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1360 180180 360 x-1 48. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1360 180180 360 x-1 49. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1360 180180 360 x-1 50. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1360 180180 360 x-1 51. yy tan x360180 180 360540 720 x domain: all real x except x 90 180k , where k is an integer range: all real y odd functionperiod: 180 y y cosecxtan x tan x 1Exercise 4D; 3ace etc,360 180180 360 x 4bdf etc, 5ace etc,-1 6bdf, 7ace, 8b, 9bd,10bd, 11ac, 13 ace etc, 14c, 16*