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education/math/MATH1060 (trig)/Graphing.md
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@ -49,7 +49,7 @@ Interpreting the above table:
- When $x = \frac{\pi}{4}$, $y = 1$ - When $x = \frac{\pi}{4}$, $y = 1$
- When $x = \frac{\pi}{2}$, there's an asymptote - When $x = \frac{\pi}{2}$, there's an asymptote
Without any transformations applied, the period of $tan(x) = 1$. Because $tan$ is an odd function, $tan(-x) = -tan(x)$. Without any transformations applied, the period of $tan(x) = \pi$. Because $tan$ is an odd function, $tan(-x) = -tan(x)$.
# Cotangent # Cotangent
$$ y = cot(x) $$ $$ y = cot(x) $$
![Graph of cotangent](assets/graphcot.svg) ![Graph of cotangent](assets/graphcot.svg)
@ -62,3 +62,10 @@ If $cot(x) = \frac{cos(x)}{sin(x)}$, then:
| ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- | | ----------------------------------------- | ----------------------------------------- | ---------------------------------------------------------------- |
| $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cot(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ | | $sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ | $cot(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2} = 1$ |
| $sin(\frac{\pi}{2}) = 1$ | $cos(\frac{\pi}{2}) = 0$ | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$ | | $sin(\frac{\pi}{2}) = 1$ | $cos(\frac{\pi}{2}) = 0$ | $tan(\frac{\pi}{2}) = \frac{1}{0} = DNF$ |
Without any transformations applied, the period of $cot(x) = \pi$. Because $cot$ is an odd function, $cot(-x) = -cot(x)$.
# Examples
> Given $-2tan(\pi*x + \pi) - 1$
- $A = -2, B = \pi, C = -\pi, D = -1$
-