diff --git a/education/math/MATH1060 (trig)/Graphing.md b/education/math/MATH1060 (trig)/Graphing.md index ee9b1f0..b2f361c 100644 --- a/education/math/MATH1060 (trig)/Graphing.md +++ b/education/math/MATH1060 (trig)/Graphing.md @@ -104,12 +104,21 @@ $A$, $B$, $C$, and $D$ will have similar meanings to the cosecant function as th - 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} + {} +- The vertical asymptotes of secant occur at $x = \frac{C}{B} + \frac{\pi}{2} + \frac{\pi}{2} + \frac{\pi}{|B|}k$, where $k$ is an integer. +- The vertical asymptotes of cosecant occur at $x = \frac{C}{B} + \frac{\pi}{|B|}k$, where $k$ is an integer. +- The vertical shift is $D$. # Examples > Given $-2\tan(\pi*x + \pi) - 1$ $A = -2$, $B = \pi$, $C = -\pi$, $D = -1$ - + +> Identify the vertical stretch/compress factor, period, phase shift, and vertical shift of the function $y = 4\sec(\frac{\pi}{3}x - \frac{\pi}{2}) + 1$ + +$A = 4$, $B = \frac{\pi}{3}$, $C = \frac{\pi}{2}$, $D = 4$ + +Vertical stretch: $|4| = 4$ +Period: $\frac{2\pi}{\frac{\pi}} + | Transformation | Equation | | -------------- | ------------------------- | | Stretch | $\|-2\| = 2$ |