Graphs of Sine and Cosine Func3ons Anima&on 3
y = 2sin x 2
y = sin x 1
-π
-0.5π
0
-1
-2
-3
0.5π
π
1.5π
2π
2.5π
3π
3.5π
4π
y = d + a sin ( bx – c ) y = d + a cos ( bx – c ) IaI amplitute d ver3cal shiB 2π period b c horizontal shiB b 3
y = 3cosx
2
y = cosx
1
y = 1/2cosx
-2π
-1.6π
-1.2π
-0.8π
-0.4π
0
-1
-2
-3
0.4π
0.8π
1.2π
1.6π
2π
2
y = sinx
y = sin x/2
1
-2.4π
-2π
-1.6π
-1.2π
-0.8π
-0.4π
0
-1
-2
0.4π
0.8π
1.2π
1.6π
2π
2.4π
1
•a =
2
• !π!
→
Example: 1.6
3
y = sinx 0.8
y = ½ sin (x – π/3 ) -1.5π
-π
-0.5π
0
-0.8
-1.6
y = ½ sinx 0.5π
π
1.5π
Example: •reflection on x − axis
•a =3
2π
•period =
=1
2π
•←##
4π #
2π
=2
5
y = -­‐3cos(2πx) y = -­‐3cos(2πx + 4π) 2.5
y = cosx -π
-0.75π
-0.5π
-0.25π
0
0.25π
y = -­‐ cosx -2.5
y = -­‐3cosx -5
0.5π
0.75π
π
Example: •a =3
y = 2 + 3cos2x •period =
5
•↑ 2
y = 3cosx 2.5
y = cosx -1.5π
-π
-0.5π
0
-2.5
y = 3cos2x 0.5π
π
1.5π
2π
=π
2