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6.1 inverse trig functions

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6.1 inverse trig functions

1. 1. Inverse Sine, Cosine, and Tangent Functions *One-to-One Function 6.1 Inverse Trigonometric Functions
2. 2. Function and One-to-One Function One-to-one  For each x, there is exactly one y.  The graph “passes” the vertical line test.  For each y, there is exactly one x.  The graph “passes” the horizontal line test.  If a function is one-to- one, the inverse will also be a function.
3. 3. Inverse -  The relation obtained by interchanging the x and y values of a function.  The inverse of a function that is NOT one-to-one can be made a function by limiting the domain of the original function to make it one-to-one.  The domain of a function is the range of its inverse.  The range of a function is the domain of its inverse.
4. 4. Graph 2 2siny x x     -2 -1 2 1 -2 -1 21 1 siny x 
5. 5. Graph cos 0y x x    -1 4321 3 -1 2 1 1 cosy x 
6. 6. Graph 2 2tany x x     -2 -1 2 1 -2 -1 21 1 tany x 
7. 7. Evaluate – exact value  1 1 2sin
8. 8. Evaluate – exact value  1 2 2sin 
9. 9. Evaluate – exact value  1 cos 0
10. 10. Evaluate – exact value  1 1 2cos 
11. 11. Evaluate – exact value  1 tan 1
12. 12. Evaluate – exact value  1 tan 3 
13. 13. Evaluate - approximation 1 sin 0.37  1 cos 0.82   1 tan 4.21  0.38 2.53 1.34 
14. 14. 1 3 2cos cos     1 6sin sin     
15. 15. 1 cos cos 0.75    1 9sin sin    
16. 16. p. 457 # 1 - 4, 13 - 44 Assignment