From 5a3c1486fb59e5cbc8bc0c129f3b9bae497e8bf5 Mon Sep 17 00:00:00 2001
From: zleyyij <75810274+zleyyij@users.noreply.github.com>
Date: Mon, 30 Sep 2024 11:28:24 -0600
Subject: [PATCH] vault backup: 2024-09-30 11:28:24

---
 education/math/MATH1060 (trig)/Graphing.md | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/education/math/MATH1060 (trig)/Graphing.md b/education/math/MATH1060 (trig)/Graphing.md
index 4282039..a41a6cf 100644
--- a/education/math/MATH1060 (trig)/Graphing.md	
+++ b/education/math/MATH1060 (trig)/Graphing.md	
@@ -69,8 +69,15 @@ Without any transformations applied, the period of $cot(x) = \pi$. Because $cot$
 Given the form $y = A\tan(Bx - C) + D$ (the same applies for $\cot$)
 - The stretching factor is $|A|$
 - The period is $\frac{\pi}{|B|}$
-- The domain of $tan$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + {\pi}{|}$
+- The domain of $tan$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + {\pi}{|B|}k$, where $k$ is an integer. (everywhere but the asymptotes)
+- The domain of $cot$ is all of $x$, where $x \ne \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer (everywhere but the asymptotes)
+- The range of both is $(-\infty, \infty)$
+- The phase shift is $\frac{C}{B}$
+- The vertical shift is $D$
 # Examples
 > Given $-2tan(\pi*x + \pi) - 1$
 - $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$
-- Stretch 
\ No newline at end of file
+- Stretch: $|-2| = 2$
+- Period: $\frac{\pi}{|\pi|} = 1$
+- Phase shift: $\frac{-\pi}{\pi} = -1$
+- Vertical shift: $
\ No newline at end of file