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education/math/MATH1060 (trig)/Graphing.md
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@ -110,8 +110,19 @@ $A$, $B$, $C$, and $D$ will have similar meanings to the cosecant function as th
# Inverse Functions # Inverse Functions
For any one to one function $f(x) = y$, a function $f^{-1}(y) = x)$. A function is considered one-to-one if every input only has one output, and every output can only be created from a single input. For any one to one function $f(x) = y$, a function $f^{-1}(y) = x)$. A function is considered one-to-one if every input only has one output, and every output can only be created from a single input.
The inverse of a trig function is denoted as $sin^{-1}$, or $arcsin$ respectively.
The inverse of a trig function is **not** the same as the reciprocal of a trig function, $\frac{1}{sin}$ is not the same as $sin
- The *domain* of $f$ is the *range* of $f^{-1}$. - The *domain* of $f$ is the *range* of $f^{-1}$.
- The *range* of $f$ is the *domain* of $f^{-1}$. - The *range* of $f$ is the *domain* of $f^{-1}$.
| Trig functions | Inverse trig functions |
| ----------------------------------- | ------------------------------------ |
| Domain: Angle measures | Domain: Ratio of sides of a triangle |
| Range: Ratio of sides of a triangle | Range: Angle Measure |
| | |
# Examples # Examples
> Given $-2\tan(\pi*x + \pi) - 1$ > Given $-2\tan(\pi*x + \pi) - 1$