689 B
689 B
Given the above graph:
- At the origin,
sin(x) = 0andcos(x) = 1 - A full wavelength takes
2\pi
Manipulation
| Formula | Movement |
|---|---|
y = cos(x) - 1 |
Vertical shift down by 1 |
y = 2cos(x) |
Vertical stretch by a factor of 2 |
y = -cos(x) |
Flip over x axis |
y = cos(2x) |
Horizontal shrink by a factor of 2 |
Periodic Functions
A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a period.