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Graphing Sine and Cosine

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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 = - –X max = 3 –X scale = /6 Window— –Y min =-3 –Y max = 3 –Y scale =.5

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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 +1) 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 -1) 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 |A| Period 2 |B| Vertical Shift up/down Horizontal Shift Left/Right C B

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

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Examples-- y = 3sin (x + 1) -3 Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ y = cos (x - 2) Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

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y = sin (2x) Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ y = ½ cos (½ x) + 1 Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________

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y = 2 sin (2x + 3) Amp.= _______ Period = _____ Horizontal Phase Shift = _________ Vertical Phase Shift = ________ y = ½ cos (3x +1) + 1 Amp.= _______ 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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y = A sin (Bx – C) + D Intercept Maximum Intercept Minimum Intercept Unless A = Negative # Intercept Minimum Intercept Maximum Intercept

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y = A cos (Bx – C) + D Maximum Intercept Minimum Intercept Maximum Unless A = Negative # Minimum Intercept Maximum Intercept Minimum

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Graphing by Key Points y = 2 sin x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( /2, ) ( , ) (3 /2, ) (2 , )

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Graphing by Key Points y = -2 cos x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( /2, ) ( , ) (3 /2, ) (2 , )

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Graphing by Key Points y = sin 4x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( /8, ) ( /4, ) (3 /8, ) ( /2, )

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Graphing by Key Points y = 3 cos 1 / 2 x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( , ) (2 , ) (3 , ) (4 , )

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Graphing by Key Points y = 3 sin x +2 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( /2 ) ( , ) (3 /2, ) (2 , )

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Graphing by Key Points y = sin x +2 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) ( /2 ) ( , ) (3 /2, ) (2 , )

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Graphing by Key Points y = cos (x + ) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (- , ) (- /2 ) (0, ) ( /2, ) ( , )

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Graphing by Key Points y = sin (x - /4) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ ( /4, ) (3 /4, ) (5 /4, ) (7 /4, ) (9 /4, )

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Graphing by Key Points y = 4sin (x/2 + /2) Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (- , ) (0, ) ( , ) (2 , ) (3 , )

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Graphing by Key Points y = -cos x Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ (0, ) (1/2, ) (1, ) (3/2, ) (2, )

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Graphing by Key Points y = 2sin (x/2 - /2) -1 Amp = _________ Horizontal Shift = _______ Period = _______ Vertical Shift = _________ Inc. = ________ ( , ) (2 , ) (3 , ) (4 , ) (5 , )

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Honors Trig– HW Page 176 (27-44 all) Regular Trig– HW Page 137 (23-44 all)

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Translations of sine and cosine graphs The graph will be shifted to the right by c. The graph will be shifted up d. We already know what A and B are used.

Translations of sine and cosine graphs The graph will be shifted to the right by c. The graph will be shifted up d. We already know what A and B are used.

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