Chapter 8-Section 3

In this lesson we use our prior knowledge from lesson 1 and 2 to carry out the process. Sin and Cos are both involved in the process. We also use the amplitude and period. Amplitude- distance from 0 to highest point, 1/2 the vertical distance.

• The absolute value of A=amplitude
• To find the period use 2π/B

y=Asin(Bx±C)±D or y=Acos(B±C)±D (plug into this formula)

To graph:
• Follow period change with 5 points.
1.0
2.π/2
3.π
4.3π/2
5.2π

• Then add or subract C from those 5 points. (if the eqaution is + C you subtract and vice versa)

• Move all y values up D or down P (if + then up)

When looking at a graph and making an equation, we use a new formula to find amplitude.

-max-min/2= amplitude

y=4sin(πx-1/2)+1
amplitude=4 and period= 2

1.0= 0/π=0 + ½= ½
2.π/2= (π/2) / (1/ π)=1/2+1/2=1
3.3 π/2=(3 π/2)/ (1/ π)=(3/2)+(1/2)=3/2
4.π= π/ π=1 + ½=2
5.2 π=2 π / π=2 +1/2=5/2