2024-09-23 17:51:45 +00:00
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Given the above graph:
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- At the origin, $sin(x) = 0$ and $cos(x) = 1$
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- A full wavelength takes $2\pi$
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# Manipulation
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2024-09-23 18:01:19 +00:00
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| Formula | Movement |
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| ---------------- | ---------------------------------- |
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| $y = cos(x) - 1$ | Vertical shift down by 1 |
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| $y = 2cos(x)$ | Vertical stretch by a factor of 2 |
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| $y = -cos(x)$ | Flip over x axis |
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| $y = cos(2x)$ | Horizontal shrink by a factor of 2 |
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# Periodic Functions
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A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a *period*.
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