Equations For 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 = 0
Slide 5
Graph the equation y = 2 Sin x 22 1 -2 Key Points:0 Value: 0
20-20 22 2
Slide 6
Amplitude (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 x y = Cos x y = -2 Sin x
Slide 7
22 4 -4 y = 4 Sin x y = Cos x 3 2 1 -2 -3 y = -2Sin x
Slide 8
y = a Sin (bx c) + d b gives us the period of the curve Period
= y = 4 Sin 2x Amplitude = Period = 4 =
Slide 9
Key Points Would having a period of change the key points of
the curve? 22 1
Slide 10
Finding Key Points In GeneralFor Y = 4Sin 2x 1) Find the period
of the curve 2) Divide the period into 4 equal parts 3) From your
starting point, add this distance 4 times for each period 1) Period
= 2) Distance = 3) 0,,,,
Slide 11
1 y = 4Sin 2x 4 -4
Slide 12
Graph the following curves y = 4 Cos 8x y = Cos 2 x y = -2 Sin
6x
Slide 13
y = 4Cos 8x Amplitude =4b =8 Period = Distance = 4 -4
Slide 14
y = Cos 2 x Amplitude =b = 22 Period = Distance = -
Slide 15
y = -2Sin 6x Amplitude =2b =6 Period = Distance = 2 - 2
Slide 16
y = a Sin (bx c) + d a = b = c = amplitude Find the period Find
the phase shift horizontal shift
Slide 17
y = Sin (x - ) a = b = c = 1 Period = P. S. =
Slide 18
y = -3 Cos (2 x + 4 ) a = b = c = 3 22 Period = P. S. =
Slide 19
y = a Sin (bx c) + d a = b = c = d = amplitude Find the period
Find the phase shift Vertical Shift