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

@@ -104,12 +104,21 @@ $A$, $B$, $C$, and $D$ will have similar meanings to the cosecant function as th
 - The domain of secant is all $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + \frac{\pi}{|B|}k$, where $k$ is an integer. (Every half period + phase shift is where asymptotes appear)
 - The domain of cosecant is all $x$, where $x \ne \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer.
 - The range is $(\infty, -|A| +D]\cup [|A| + D], \infty)$
-- The  vertical asymptotes of secant occur at $x = \frac{C}{B} + {}
+- The vertical asymptotes of secant occur at $x = \frac{C}{B} + \frac{\pi}{2} + \frac{\pi}{2} + \frac{\pi}{|B|}k$, where $k$ is an integer.
+- The vertical asymptotes of cosecant occur at $x = \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer.
+- The vertical shift is $D$. 
 # Examples
 > Given $-2\tan(\pi*x + \pi) - 1$
 
  $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$
 
+> Identify the vertical stretch/compress factor, period, phase shift, and vertical shift of the function $y = 4\sec(\frac{\pi}{3}x - \frac{\pi}{2}) + 1$ 
+
+$A = 4$, $B = \frac{\pi}{3}$, $C = \frac{\pi}{2}$, $D = 4$
+
+Vertical stretch: $|4| = 4$
+Period: $\frac{2\pi}{\frac{\pi}}
+
 | Transformation | Equation                  |
 | -------------- | ------------------------- |
 | Stretch        | $\|-2\| = 2$              |