diff --git a/education/math/MATH1060 (trig)/Graphing.md b/education/math/MATH1060 (trig)/Graphing.md index 7d7a4e1..80d780d 100644 --- a/education/math/MATH1060 (trig)/Graphing.md +++ b/education/math/MATH1060 (trig)/Graphing.md @@ -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: $$ y = A\sec(B{x} - C) + D $$ -$A$, $B$, $C$, 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 $$ y = \csc(x) $$ @@ -92,11 +92,16 @@ $$ y = \csc(x) $$ $$ \csc(x) = \frac{1}{\sin(x)} $$ -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: -$$ y = A\sec(B{x} - C) + D $$ -$A$, $B$, $C$, and $D$ will have similar meanings to the secant functions as they did to the sine and cosine functions. +The general form of cosecant is: +$$ y = A\scsc(B{x} - C) + D $$ +$A$, $B$, $C$, 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. # Examples > Given $-2\tan(\pi*x + \pi) - 1$