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