Graphs of Sine and Cosine

Section 4.5Graphs of Sine and CosineSine CurveKey Points:0Value:010-102

2

1-1Cosine CurveKey Points:0Value:10-1012

2

1-1EquationsFor the rest of this section, we will be graphing:

y = a Sin (bx c) + d

y = a Cos (bx c) + d

y = Sin x a = 1 b = 1 c = 0 d = 0Graph the equation y = 2 Sin x2

1-2Key Points:0Value:020-202

2-1Amplitude (a)Half the distance between the maximum and minimum values of the function

Given by the value of a

Graph the functions:y = 4 Sin xy = Cos xy = -2 Sin x2

4-4y = 4 Sin xy = Cos x321-1-2-3y = -2Sin xy = a Sin (bx c) + db gives us the period of the curvePeriod =

y = 4 Sin 2xAmplitude = Period = 4

= Key PointsWould having a period of change the key points of the curve?2

1-1Finding Key PointsIn GeneralFor Y = 4Sin 2xFind the period of the curve

Divide the period into 4 equal parts

From your starting point, add this distance 4 times for each periodPeriod =

Distance =

0, , , ,

1-1

y = 4Sin 2x4-4Graph the following curvesy = 4 Cos 8x

y = Cos 2x

y = -2 Sin 6xy = 4Cos 8xAmplitude = 4b = 8 Period =

Distance =

4-4

y = Cos 2xAmplitude = b = 2 Period =

Distance =

-

y = -2Sin 6xAmplitude = 2 b = 6 Period =

Distance =

2 - 2

y = a Sin (bx c) + da = b =

c = amplitudeFind the period

Find the phase shift horizontal shift

y = Sin (x - ) a =

b =

c =

1 Period =

P. S. =

y = -3 Cos (2x + 4) a =

b =

c = 3

2 Period =

P. S. =

y = a Sin (bx c) + da = b =

c = d = amplitudeFind the period

Find the phase shift

Vertical Shifty =a =

b =

c =

d = 2

Period =

P. S. =

3 y =a =

b =

c =

d = 4

Period =

P. S. =

-214

2-6-2

y =-2