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education/math/MATH1060 (trig)/Graphing.md
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@ -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 $\cot$) Given the form $y = A\tan(Bx - C) + D$ (the same applies for $\cot$)
- The stretching factor is $|A|$ - The stretching factor is $|A|$
- The period is $\frac{\pi}{|B|}$ - 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 # Examples
> Given $-2tan(\pi*x + \pi) - 1$ > Given $-2tan(\pi*x + \pi) - 1$
- $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$ - $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$
- Stretch - Stretch: $|-2| = 2$
- Period: $\frac{\pi}{|\pi|} = 1$
- Phase shift: $\frac{-\pi}{\pi} = -1$
- Vertical shift: $