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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   1  x
                   3
             3 x  3
Graphing Inverse
        Trig Functions
                    x
e.g i  y  5 sin
                1

                    3
Domain:  1   1  x
                   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   1  x                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   1  x                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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12X1 T05 03 graphing inverse trig (2010)

  • 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   1 x 3 3 x  3
  • 4. Graphing Inverse Trig Functions x e.g i  y  5 sin 1 3 Domain:  1   1 x 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   1 x 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   1 x 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