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# Hprec7.1

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### Hprec7.1

1. 1. 7.1: Graphs of the Sine, Cosine & Tangent Functions © 2008 Roy L. Gover(www.mrgover.com) Learning Goals: •Graph Trig functions •Analyze and interpret Trig graphs
2. 2. Example Using a table of values, graph siny t= for 2 2tπ π− ≤ ≤ 2π− 3 2π− π− 2π− 0 2π π 3 2π 2π
3. 3. Try This Using a table of values, graph cosy t= for 2 2tπ π− ≤ ≤ 2π− 3 2π− π− 2π− 0 2π π 3 2π 2π
4. 4. 2π− Solution 2π0 t
5. 5. Example Using your graphing calculator, graph ( ) cosg t t= on the interval [ ]3 ,2π π−
6. 6. Try ThisOn a sheet of paper, compare and contrast the graphs:siny t= cosy t=
7. 7. Example cosy t= 1 -1 0 Animate
8. 8. Example sint Without using your graphing calculator, find all values of t for which is 1.
9. 9. Try This cost Without using your graphing calculator, find all values of t for which is 1. 0 2t kπ= + k=integer
10. 10. ExampleWithout using your calculator, find all values of t between 0 and 2 for which π sint = 1 2 2π0 1 2
11. 11. Try This Without using your calculator, find all values of t between 0 and 2 for which π cost= 1 2 5 , 3 3 t π π =
12. 12. Analysis ( ) cosf t t=For : •What is the domain and range? •What is the unit of measure for the t and axes?( )f t
13. 13. Definition The Domain of a function is all possible values of the independent variable (t,x,θ) The Range of a function is all possible values of the dependent variable , ( ), ( )y f t f θ
14. 14. Analysis ( ) cosf t t=( ) sinf t t= Compare and contrast the two graphs. +1 -1
15. 15. Try This What is wrong with these statements: 3 cos 2 t = − sin 2t =
16. 16. Try This Graph the function : ( ) tanf x x= using your graphing calculator
17. 17. Solution ( ) tanf x x= What is the domain and range? What are Asymptotes and where do they occur?
18. 18. Important Idea Asymptotes occur at all points in the domain where the function is not defined. (0,-1) (-1,0) (1,0) (0,1)
19. 19. Important Idea Asymptotes occur at all points in the domain where the function is not defined. (0,-1) (-1,0) (1,0) (0,1)
20. 20. Try ThisCompare and contrast the graphs: siny t= − siny t= 1 -1
21. 21. Try ThisCompare and contrast the graphs: siny t= sin 1.5y t= + 2.5 1
22. 22. Example For what values of t on the interval [ ]2 ,2π π− is: ( )f t• increasing • decreasing( )f t • ( ) 0f t < 2π− 2π ( ) cosf t t=
23. 23. Example 0 cos 1t< < For what values of t on the interval [ ]3 ,2π π− is: 3π− 2π ( ) cosf t t=
24. 24. Example 3 cos 2 t = − For what values of t on the interval [ ]2 ,2π π− is: 2π− 2π ( ) cosf t t= 3 2 −
25. 25. Example 3 cos 2 t = − Name all, exact values of t for which ( ) cosf t t= 3 2 −
26. 26. Try This 1 sin 2 t = Name all, exact values of t for which 1 2 ( ) sinf t t= 2 6 t n π π= + 5 2 6 t n π π= + or
27. 27. Lesson Close Define: •Domain •Range