vault backup: 2024-09-23 12:01:18

education/math/MATH1060 (trig)/Graphing.md

@@ -5,6 +5,13 @@ Given the above graph:
 - A full wavelength takes $2\pi$
 
 # Manipulation
-| Formula            | Movement |
-| ------------------ | -------- |
-| $ y = cos(x) - 1 $ |          |
+| 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*.
+
+