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12 x1 t05 03 graphing inverse trig (2012)

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Nigel Simmons
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Graphing Inverse Trig Functions
Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3
Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3 Domain:  1  x  1 3 3 x  3
Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3 Domain:  1  x  1 3 3 x  3 Range:    y   2 5 2 5 5   y 2 2
Graphing Inverse Trig Functions x e.g i  y  5 sin 1 y 3 Domain:  1  x  1 5 3 2 3 x  3 Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
Graphing Inverse Trig Functions x e.g i  y  5 sin 1 y 3 1 x Domain:  1  x  1 5 y  5 sin 3 3 2 3 x  3 Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
ii  y  tan 1  3  x 2 
ii  y  tan 1  3  x 2  Domain: 3  x 2  0  3x 3
ii  y  tan 1  3  x 2  Domain: 3  x 2  0  3x 3 Range: x  3, y  tan 1 0 0
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
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
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
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
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
(iii ) y  sin 1 sin x
(iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x
(iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x   Range:   y 2 2
(iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x y   Range:   y 2 2  2   x   2
(iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x y   Range:   y 2 2  y  sin 1 sin x 2   x   2
(iv) y  sin sin 1 x
(iv) y  sin sin 1 x Domain:  1  x  1
(iv) y  sin sin 1 x Domain:  1  x  1 Range: when x  1, y  sin sin 1 1   sin 2 1
(iv) y  sin sin 1 x Domain:  1  x  1 Range: when x  1, y  sin sin 1 1   sin 2 1 when x  1, y  sin sin 1  1    sin    2  1
(iv) y  sin sin 1 x Domain:  1  x  1 Range: 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
y (iv) y  sin sin 1 x Domain:  1  x  1 1 Range: 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
y (iv) y  sin sin 1 x Domain:  1  x  1 y  sin sin 1 x 1 Range: 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
y (iv) y  sin sin 1 x Domain:  1  x  1 y  sin sin 1 x 1 Range: 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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12 x1 t05 03 graphing inverse trig (2012)

  • 2. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3
  • 3. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3 Domain:  1  x  1 3 3 x  3
  • 4. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3 Domain:  1  x  1 3 3 x  3 Range:    y   2 5 2 5 5   y 2 2
  • 5. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 y 3 Domain:  1  x  1 5 3 2 3 x  3 Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
  • 6. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 y 3 1 x Domain:  1  x  1 5 y  5 sin 3 3 2 3 x  3 Range:    y   -3 3 x 2 5 2 5 5 5   y  2 2 2
  • 7. ii  y  tan 1  3  x 2 
  • 8. ii  y  tan 1  3  x 2  Domain: 3  x 2  0  3x 3
  • 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. 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. 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. 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. 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. 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. (iii ) y  sin 1 sin x
  • 16. (iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x
  • 17. (iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x   Range:   y 2 2
  • 18. (iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x y   Range:   y 2 2  2   x   2
  • 19. (iii ) y  sin 1 sin x Domain:  1  sin x  1 all real x y   Range:   y 2 2  y  sin 1 sin x 2   x   2
  • 20. (iv) y  sin sin 1 x
  • 21. (iv) y  sin sin 1 x Domain:  1  x  1
  • 22. (iv) y  sin sin 1 x Domain:  1  x  1 Range: when x  1, y  sin sin 1 1   sin 2 1
  • 23. (iv) y  sin sin 1 x Domain:  1  x  1 Range: when x  1, y  sin sin 1 1   sin 2 1 when x  1, y  sin sin 1  1    sin    2  1
  • 24. (iv) y  sin sin 1 x Domain:  1  x  1 Range: 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. y (iv) y  sin sin 1 x Domain:  1  x  1 1 Range: 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. y (iv) y  sin sin 1 x Domain:  1  x  1 y  sin sin 1 x 1 Range: 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. y (iv) y  sin sin 1 x Domain:  1  x  1 y  sin sin 1 x 1 Range: 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