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12 x1 t05 03 graphing inverse trig (2012)

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  • Unfortunately the NSW HSC does not have statistics in its course and veryt little work on vectors, so sorry about that.

    I am pleased, however, that you have found somw of the slideshows useful.

    All the best in the IB
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  • hi nigel, i must say you are an excellent teacher. i am an ib student and i also have some problems with vectors and mainly statistics. if you have any matreial concerning these topics it would be very helpful of you.
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12 x1 t05 03 graphing inverse trig (2012)

  1. 1. Graphing Inverse Trig Functions
  2. 2. Graphing Inverse Trig Functions xe.g i  y  5 sin 1 3
  3. 3. Graphing Inverse Trig Functions xe.g i  y  5 sin 1 3Domain:  1  x  1 3 3 x  3
  4. 4. Graphing Inverse Trig Functions xe.g i  y  5 sin 1 3Domain:  1  x  1 3 3 x  3Range:    y   2 5 2 5 5   y 2 2
  5. 5. Graphing Inverse Trig Functions xe.g i  y  5 sin 1 y 3Domain:  1  x  1 5 3 2 3 x  3Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
  6. 6. Graphing Inverse Trig Functions xe.g i  y  5 sin 1 y 3 1 xDomain:  1  x  1 5 y  5 sin 3 3 2 3 x  3Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
  7. 7. ii  y  tan 1  3  x 2 
  8. 8. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3
  9. 9. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 Range: x  3, y  tan 1 0 0
  10. 10. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 Range: x  3, y  tan 1 0 0 x   3, y  tan 1 0 0
  11. 11. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 Range: x  3, y  tan 1 0 0 x   3, y  tan 1 0 0 x  0, y  tan 1 3   3
  12. 12. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 Range: x  3, y  tan 1 0 0 x   3, y  tan 1 0 0 x  0, y  tan 1 3   3  0 y 3
  13. 13. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 y Range: x  3, y  tan 1 0  3 0 x   3, y  tan 1 0 0 x  3 3 x  0, y  tan 1 3   3  0 y 3
  14. 14. ii  y  tan 1  3  x 2 Domain: 3  x 2  0  3x 3 y Range: x  3, y  tan 1 0   y  tan 1 3  x 2  3 0 x   3, y  tan 1 0 0 x  3 3 x  0, y  tan 1 3   3  0 y 3
  15. 15. (iii ) y  sin 1 sin x
  16. 16. (iii ) y  sin 1 sin xDomain:  1  sin x  1 all real x
  17. 17. (iii ) y  sin 1 sin xDomain:  1  sin x  1 all real x  Range:   y 2 2
  18. 18. (iii ) y  sin 1 sin xDomain:  1  sin x  1 all real x y  Range:   y 2 2  2   x   2
  19. 19. (iii ) y  sin 1 sin xDomain:  1  sin x  1 all real x y  Range:   y 2 2  y  sin 1 sin x 2   x   2
  20. 20. (iv) y  sin sin 1 x
  21. 21. (iv) y  sin sin 1 xDomain:  1  x  1
  22. 22. (iv) y  sin sin 1 xDomain:  1  x  1Range: when x  1, y  sin sin 1 1   sin 2 1
  23. 23. (iv) y  sin sin 1 xDomain:  1  x  1Range: when x  1, y  sin sin 1 1   sin 2 1 when x  1, y  sin sin 1  1    sin    2  1
  24. 24. (iv) y  sin sin 1 xDomain:  1  x  1Range: when x  1, y  sin sin 1 1   sin 2 1 when x  1, y  sin sin 1  1    sin    2  1 when x  0, y  sin sin 1 0  sin 0 0 1  y  1
  25. 25. y(iv) y  sin sin 1 xDomain:  1  x  1 1Range: when x  1, y  sin sin 1 1 -1 1 x   sin -1 2 1 when x  1, y  sin sin 1  1    sin    2  1 when x  0, y  sin sin 1 0  sin 0 0 1  y  1
  26. 26. y(iv) y  sin sin 1 xDomain:  1  x  1 y  sin sin 1 x 1Range: when x  1, y  sin sin 1 1 -1 1 x   sin -1 2 1 when x  1, y  sin sin 1  1    sin    2  1 when x  0, y  sin sin 1 0  sin 0 0 1  y  1
  27. 27. y(iv) y  sin sin 1 xDomain:  1  x  1 y  sin sin 1 x 1Range: when x  1, y  sin sin 1 1 -1 1 x   sin -1 2 1 when x  1, y  sin sin 1  1    sin    2  1 Exercise 1C; 2 to 5ace, when x  0, y  sin sin 1 0 6a b i,iii, 9, 11 to 15  sin 0 0 1  y  1

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