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

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

Graphing Sine and Cosine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 = ________

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 = ________

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 = ________

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

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 

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 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Similar presentations