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Graphing Sine and Cosine. Video Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max.

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Presentation on theme: "Graphing Sine and Cosine. Video Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max."— Presentation transcript:

1 Graphing Sine and Cosine

2 Video

3 Graphing Calculator Mode— Radians Par Simul Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -3 –Y max = 3 –Y scale = 1 Window— –T min = 0 –T max = 2  –T step =.1

4 Press Y= x 1T = cos (T) y 1T = sin (T) x 2T = T y 2T = sin (T) Press Graph

5 Using the Graphing Calculator Mode— Radians Function Sequential Window— –X min = -1 –X max = 2  –X scale =  /2 Window— –Y min = -10 –Y max = 10 –Y scale = 1

6 Press Y= y 1 = sin (X) y 2 = 3sin (X) Press Graph

7 Press Y= y 1 = sin (X) y 2 = 4sin (X) Press Graph

8 Press Y= y 1 = sin (X) y 2 = -4sin (X) Press Graph

9 Press Y= y 1 = sin (X) y 2 = sin (X) +1 Press Graph

10 Press Y= y 1 = sin (X) y 2 = sin (X) -2 Press Graph

11 Press Y= y 1 = sin (X) y 2 = sin (X -  ) Press Graph

12 Press Y= y 1 = sin (X) y 2 = sin (X – 1/2  ) Press Graph

13 Press Y= y 1 = sin (X) y 2 = sin (2X) Press Graph

14 Press Y= y 1 = sin (X) y 2 = sin (2X) Press Graph

15 Press Y= y 1 = sin (X) y 2 = sin (1/2x) Press Graph

16 Y = A sin (Bx ± C) ± D Amplitude Period Change 2  |b| Vertical Shift up/down Horizontal Shift Left/Right C B

17 Examples-- Y = 3sin (x +  ) -3 A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ Y = cos (x - 2  ) A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

18 Y = -2sin (2x) A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ Y = -½ cos (½ x) + 1 A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

19 Y = -2 sin (2x + 3  ) A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ Y = ½ cos (3x +  ) + 1 A= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

20 End of day 1 Honors Trig– HW Page 176 (1-26 all) Reg. Trig– HW Page 136 (1-22 all)

21 Graphing Sine Curve Y = sin (x) 0  /6  /4  /3  /2 2  /3 3  /4 5  /6  7  /6 5  /4 4  /3 3  /2 5  /3 7  /4 11  /6 2 

22 Graphing Cosine Curve Y = cos (x) 0  /6  /4  /3  /2 2  /3 3  /4 5  /6  7  /6 5  /4 4  /3 3  /2 5  /3 7  /4 11  /6 2 

23 Graphing by Key Points Y = 2 sin x A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

24 Graphing by Key Points Y = -2 cos x A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

25 Graphing by Key Points Y = sin 4x A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /4, ) (  /2, ) (3  /4, ) ( , )

26 Graphing by Key Points Y = 3 cos 1/2x A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) ( , ) (2 , ) (3 , ) (4 , )

27 Graphing by Key Points Y = 2 sin x A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

28 Graphing by Key Points Y = sin x +2 A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

29 Graphing by Key Points Y = sin (x -  /4) A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

30 Graphing by Key Points Y = cos (x +  ) A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

31 Graphing by Key Points Y = 4sin (x/2 +  /2) A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

32 Graphing by Key Points Y = -cos (  x - 1/3) A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

33 Graphing by Key Points Y = 2sin (x/2 -  /2) -3 A = _________ Period = ______ Key Points -- Period ÷ 4 (0, ) (  /2, ) ( , ) (3  /2, ) (2 , )

34 Honors Trig– HW Page 176 ( all) Regular Trig– HW Page 137 ( all)


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