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Graphing Sine and Cosine

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Video

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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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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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 = ________

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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 = ________

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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 = ________

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

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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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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