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education/math/MATH1060 (trig)/Graphing.md
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@ -84,7 +84,7 @@ Because secant is the reciprocal of cosine, when $\cos{x} = 0$, then secant is u
The general form of secant is: The general form of secant is:
$$ y = A\sec(B{x} - C) + D $$ $$ y = A\sec(B{x} - C) + D $$
$A$, $B$, $C$, and $D$ will have similar meanings to the secant functions as they did to the sine and cosine functions. $A$, $B$, $C$, and $D$ will have similar meanings to the secant function as they did to the sine and cosine functions.
# Cosecant # Cosecant
$$ y = \csc(x) $$ $$ y = \csc(x) $$
@ -92,11 +92,16 @@ $$ y = \csc(x) $$
$$ \csc(x) = \frac{1}{\sin(x)} $$ $$ \csc(x) = \frac{1}{\sin(x)} $$
Because cosecant is the reciprocal of sine, when $\sin{x} = 0$, then cosecant is undefined. $|\sin$| is never *greater than* 1, so secant is never *less than* 1 in absolute value. When the graph of cosine crosses the x axis, an asymptote for a matching graph of secant will appear there. Because cosecant is the reciprocal of sine, when $\sin{x} = 0$, then cosecant is undefined. $|\sin$| is never *greater than* 1, so secant is never *less than* 1 in absolute value. When the graph of sine crosses the x axis, an asymptote for a matching graph of cosecant will appear there.
The general form of secant is: The general form of cosecant is:
$$ y = A\sec(B{x} - C) + D $$ $$ y = A\scsc(B{x} - C) + D $$
$A$, $B$, $C$, and $D$ will have similar meanings to the secant functions as they did to the sine and cosine functions. $A$, $B$, $C$, and $D$ will have similar meanings to the cosecant function as they did to the sine and cosine functions.
# Features of Secant and Cosecant
- The stretching factor is $|A|$
- The period is $\frac{2\pi}{|B|}$
- The domain of secant is all $x$, where $x \ne \frac{C}{B} + \frac{\pi}{2} + \frac{\pi}{|B}k$, where $k$ is an integer.
# Examples # Examples
> Given $-2\tan(\pi*x + \pi) - 1$ > Given $-2\tan(\pi*x + \pi) - 1$