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education/math/MATH1060 (trig)/Graphing.md

@@ -95,13 +95,16 @@ $$ \csc(x) = \frac{1}{\sin(x)} $$
 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 sine crosses the x axis, an asymptote for a matching graph of cosecant will appear there. 
 
 The general form of cosecant is:
-$$ y = A\scsc(B{x} - C) + D $$
+$$ y = A\csc(B{x} - C) + D $$
 $A$, $B$, $C$, 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.
+- 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. (Every half period + phase shift is where asymptotes appear)
+- The domain of cosecant is all $x$, where $x \ne \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer.
+- The range is $(\infty, -|A| +D]\cup [|A| + D], \infty)$
+- The  vertical asymptotes of secant occur at $x = \frac{C}{B} + {}
 # Examples
 > Given $-2\tan(\pi*x + \pi) - 1$