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.

Graphing Sine and Cosine

Video

Graphing CalculatorMode—

RadiansParSimul

• 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=x1T = cos (T)

y1T = sin (T)

x2T = T

y2T = sin (T)

Press Graph

Using the Graphing CalculatorMode—

RadiansFunctionSequential

• Window—– X min = -1– X max = 2– X scale = /2

• Window—– Y min = -10– Y max = 10– Y scale = 1

Press Y=y1 = sin (X)

y2 = 3sin (X)

Press Graph

Press Y=y1 = sin (X)

y2 = 4sin (X)

Press Graph

Press Y=y1 = sin (X)

y2 = -4sin (X)

Press Graph

Press Y=y1 = sin (X)

y2 = sin (X) +1

Press Graph

Press Y=y1 = sin (X)

y2 = sin (X) -2

Press Graph

Press Y=y1 = sin (X)

y2 = sin (X - )

Press Graph

Press Y=y1 = sin (X)

y2 = sin (X – 1/2)

Press Graph

Press Y=y1 = sin (X)

y2 = sin (2X)

Press Graph

Press Y=y1 = sin (X)

y2 = sin (2X)

Press Graph

Press Y=y1 = sin (X)

y2 = sin (1/2x)

Press Graph

Y = A sin (Bx ± C) ± D

Amplitude

Period Change

2 |b|

Vertical Shift up/down

Horizontal ShiftLeft/Right

C B

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 = ________

Y = -2sin (2x)A= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________

Y = -½ cos (½ x) + 1A= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________

Y = -2 sin (2x + 3)A= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________

Y = ½ cos (3x +) + 1A= _______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 CurveY = 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 CurveY = 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

Graphing by Key PointsY = 2 sin x

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = -2 cos x

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = sin 4x

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/4, )(/2, )

(3/4, )

(, )

Graphing by Key PointsY = 3 cos 1/2x

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(, )

(2, )

(3, )

(4, )

Graphing by Key PointsY = 2 sin x

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = sin x +2

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = sin (x - /4)

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = cos (x + )

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = 4sin (x/2 + /2)

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = -cos (x - 1/3)

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Graphing by Key PointsY = 2sin (x/2 - /2) -3

A = _________Period = ______

Key Points -- Period ÷ 4

(0, )(/2, )(, )

(3/2, )

(2, )

Honors Trig– HW Page 176 (27-44 all)

Regular Trig– HW Page 137 (23-44 all)