8-3

This week in Advanced Math we learned sections 8-1 through 8-3. All 3 sections tie into one another. They all involve sine and cosine. You also must know what amplitude and period is. Amplitude is the distance from O to the highest point. ½ is the vertical distance. Period is how long it takes a function to repeat itself. Here is a look at section 8-3.

Formulas:
y = Asin (Bx+ or – C) + or – D
y = Acos (Bx + or – C) + or – D
Amplitude = max-min/2

Here are the steps to graphs:
1. First you must follow the steps for period. (Change the 5 points)
2. Next you will add or subtract C from the 5 points.
3. Lastly you will any y values up D or down P.

Example Problem:

y = 2sin (2x – ¼) + 2

Amplitude = 2 Period = 2π/2 = π

1. 0: 0/2 = 0 + ¼ = ¼
2. π/2: π/2(½) = (π/4) + ¼ = (π + 1) / 4
3. π: π/2 = π/2 + ¼ = (2π + 1) / 4
4. 3π/2: 3π/2(1/2) = 3π/4 + ¼ = (3π + 1) / 4
5. 2π: 2π/2 = π + ¼ = (4π + 1) / 4