12 x1 t03 02 graphing trig functions (2013)
TRANSCRIPT
Graphing Trig Functions
Graphing Trig Functions
1) Sine Curve
Graphing Trig Functions
y1
-1
1) Sine Curve
Graphing Trig Functions
y
x
1
-1
1) Sine Curve
2 3 42
Graphing Trig Functions
y
x
1
-1
1) Sine Curve
2 3 42
Graphing Trig Functions
y
x
1
-1
1) Sine Curve
2 3 42
Graphing Trig Functions
y
x
1
-1
1) Sine Curve
2 3 42
Graphing Trig Functions
y
x
sin xy 1
-1
1) Sine Curve
2 3 42
Graphing Trig Functions
y
x
sin xy 1
-1
1) Sine Curve
2 3 42
x real all:domain
Graphing Trig Functions
y
x
sin xy 1
-1
1) Sine Curve
2 3 42
x real all:domain11-:range y
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
period
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
In general;
sin cbxay
units 2 periodb
period
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
In general;
sin cbxay
units 2 periodb
periodamplitude
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
In general;
sin cbxay
units 2 periodb
units amplitude a
periodamplitude
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
In general;
sin cbxay
units 2 periodb
units amplitude a
periodamplitude
4period divisions
Graphing Trig Functions
y
x
sin xy
x real all:domain11-:range y
1
-1
1) Sine Curve
2 3 42
In general;
sin cbxay
units 2 periodb
units amplitude a
periodamplitude
4period divisions
left toshift bc
e.g.
29sin5 xy
e.g.
29sin5 xy
units 9
2 period
e.g.
29sin5 xy
units 9
2 period
units 5amplitude
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y5
-5 9
92
9
x
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y5
-5 9
92
9
x
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y5
-5 9
92
9
x
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y5
-5 9
92
9
x
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y5
-5 9
92
9
x
e.g.
29sin5 xy
units 9
2 period
units 5amplitude 18
divisions
right to18
shift
y
29sin5
xy5
-5 9
92
9
x
2) Cosine Curve
2) Cosine Curve cos cbxay
2) Cosine Curve cos cbxay
units 2 periodb
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
2) Cosine Curve cos cbxay
units 2 periodb
unitsamplitude a4
period divisions
left toshift bc
e.g. 28
cos4
xy
16
81
2 period
4 amplitude
4divisions
down upsideup,2left,to8shift
y
6
-2 8 168 x
2
28
cos4
xy
3) Tangent Curve
3) Tangent Curve tan cbxay
3) Tangent Curve tan cbxay
units periodb
3) Tangent Curve tan cbxay
units periodb
2
period divisions
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift y
1 2 x
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift y
1 2 x
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift y
1 2 x
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift y
1 2 x
2tan xey
3) Tangent Curve tan cbxay
units periodb
2
period divisions
left toshift bc
e.g. 2tan xey
1
period
21 divisions
rightto2shift y
1 2 x
2tan xey
Exercise 14C; 2b, 3b,4b, 5bce, 8, 9, 10b, 13,
15, 16, 17, 20