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