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# Y = A Sin(bx+c) + d

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### Y = A Sin(bx+c) + d

1. 1. Y = ASin(bx+c) + dHow the numbers control the graph - Dave Coulson, 2012
2. 2. Y = Sin(x)The sine graph (close-up) usually looks like this.
3. 3. Y = Sin(x)This is how it would look from a distance.The graph never gets higher than 1 or lower than -1.
4. 4. Y = Sin(x) + 1I can move the graph around, however, by changing the formula.
5. 5. In this case I’ve added a 1 Y = Sin(x) + 1to the formula, and madethe graph rise by one unit.
6. 6. I can make it rise to any Y = Sin(x) + 2height I want by doing this.
7. 7. I can stretch the graph up Y = 2Sin(x) + 2and down by putting amultiplier in front of thesine function.
8. 8. The bigger the number, Y = 3Sin(x) + 2the wider the swing.
9. 9. Now watch me change the Y = 3Sin(2x) + 2frequency of the oscillation.
10. 10. The higher the frequency the Y = 3Sin(3x) + 2more oscillations.
11. 11. The higher the frequency the Y = 3Sin(4x) + 2more oscillations.
12. 12. Now watch me move the Y = 3Sin(4x+10O) + 2graph to the left.
13. 13. Now watch me move the Y = 3Sin(4x+20O) + 2graph to the left.
14. 14. I can do this by adding Y = 3Sin(4x+30O) + 2numbers to the variableinside the sine function.
15. 15. Y = 3Sin(4x+30O) + 2By moving the curve around in these ways, it’s possible to use the sinefunction to represent all kinds of things.
16. 16. Y = 3Sin(4x+30O) + 2Maybe the waves represent sound waves, or strings of photons, orpressure waves in the ground following an earthquake.
17. 17. Y = 3Sin(4x+30O) + 2The number added to the x term is called a phase shift or a phase delay.
18. 18. Y = 3Sin(4x+30O) + 2Adding a number makes the curve shift to the left.
19. 19. Y = 3Sin(4x+30O) + 2The multiplier in front of the x is called the frequency.
20. 20. Y = 3Sin(4x+30O) + 2The multiplier in front of the Sine function is called the amplitude.
21. 21. Y = 3Sin(4x+30O) + 2The number added to the back is simply a vertical shift.
22. 22. [END]