1.2 KiB
1.2 KiB
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.
Sinusoidal Functions
A function that has the same shape as a sine or cosine wave is known as a sinusoidal function.
There are 4 general functions:
A * sin(B*x - C) + D |
y = A * cos(B*x -c) + D |
|---|---|
y = A * sin(B(x - \frac{C}{B})) + D |
y = A*cos(B(x - \frac{C}{B})) + D |
How to find the:
- Amplitude:
|A| - Period:
\frac{2\pi}{B} - Phase shift:
\frac{C}{|B|} - Vertical shift:
D
y = A * \sin(B(x-\frac{C}{B}))