Compare commits
No commits in common. "6a9c9fa9d16a2588301c3208324e6ddc68d994d6" and "3eb08e7d9ea5b8c89d19a7a0cf3ce18c580c577b" have entirely different histories.
6a9c9fa9d1
...
3eb08e7d9e
4
.obsidian/file-recovery.json
vendored
4
.obsidian/file-recovery.json
vendored
@ -1,4 +0,0 @@
|
||||
{
|
||||
"intervalMinutes": 5,
|
||||
"keepDays": 7
|
||||
}
|
169
.obsidian/plugins/execute-code/data.json
vendored
169
.obsidian/plugins/execute-code/data.json
vendored
@ -1,169 +0,0 @@
|
||||
{
|
||||
"lastOpenLanguageTab": "c",
|
||||
"timeout": 10000,
|
||||
"allowInput": true,
|
||||
"wslMode": false,
|
||||
"shellWSLMode": false,
|
||||
"onlyCurrentBlock": false,
|
||||
"nodePath": "node",
|
||||
"nodeArgs": "",
|
||||
"jsFileExtension": "js",
|
||||
"jsInject": "",
|
||||
"tsPath": "ts-node",
|
||||
"tsArgs": "",
|
||||
"tsInject": "",
|
||||
"leanPath": "lean",
|
||||
"leanArgs": "",
|
||||
"leanInject": "",
|
||||
"luaPath": "lua",
|
||||
"luaArgs": "",
|
||||
"luaFileExtension": "lua",
|
||||
"luaInject": "",
|
||||
"dartPath": "dart",
|
||||
"dartArgs": "",
|
||||
"dartFileExtension": "dart",
|
||||
"dartInject": "",
|
||||
"csPath": "dotnet-script",
|
||||
"csArgs": "",
|
||||
"csFileExtension": "csx",
|
||||
"csInject": "",
|
||||
"pythonPath": "python",
|
||||
"pythonArgs": "",
|
||||
"pythonEmbedPlots": true,
|
||||
"pythonFileExtension": "py",
|
||||
"pythonInject": "",
|
||||
"shellPath": "bash",
|
||||
"shellArgs": "",
|
||||
"shellFileExtension": "sh",
|
||||
"shellInject": "",
|
||||
"batchPath": "call",
|
||||
"batchArgs": "",
|
||||
"batchFileExtension": "bat",
|
||||
"batchInject": "",
|
||||
"groovyPath": "groovy",
|
||||
"groovyArgs": "",
|
||||
"groovyFileExtension": "groovy",
|
||||
"groovyInject": "",
|
||||
"golangPath": "go",
|
||||
"golangArgs": "run",
|
||||
"golangFileExtension": "go",
|
||||
"goInject": "",
|
||||
"javaPath": "java",
|
||||
"javaArgs": "-ea",
|
||||
"javaFileExtension": "java",
|
||||
"javaInject": "",
|
||||
"maxPrologAnswers": 15,
|
||||
"prologInject": "",
|
||||
"powershellPath": "powershell",
|
||||
"powershellArgs": "-file",
|
||||
"powershellFileExtension": "ps1",
|
||||
"powershellInject": "$OutputEncoding = [console]::InputEncoding = [console]::OutputEncoding = New-Object System.Text.UTF8Encoding",
|
||||
"powershellEncoding": "latin1",
|
||||
"cargoPath": "cargo",
|
||||
"cargoEvalArgs": "",
|
||||
"rustInject": "",
|
||||
"cppRunner": "cling",
|
||||
"cppFileExtension": "cpp",
|
||||
"cppInject": "",
|
||||
"cppArgs": "",
|
||||
"cppUseMain": false,
|
||||
"clingPath": "gcc",
|
||||
"clingArgs": "",
|
||||
"clingStd": "c++17",
|
||||
"rustFileExtension": "rs",
|
||||
"RPath": "Rscript",
|
||||
"RArgs": "",
|
||||
"REmbedPlots": true,
|
||||
"RFileExtension": "R",
|
||||
"rInject": "",
|
||||
"kotlinPath": "kotlinc",
|
||||
"kotlinArgs": "-script",
|
||||
"kotlinFileExtension": "kts",
|
||||
"kotlinInject": "",
|
||||
"swiftPath": "swift",
|
||||
"swiftArgs": "",
|
||||
"swiftFileExtension": "swift",
|
||||
"swiftInject": "",
|
||||
"runghcPath": "runghc",
|
||||
"ghcPath": "ghc",
|
||||
"ghciPath": "ghci",
|
||||
"useGhci": false,
|
||||
"haskellInject": "",
|
||||
"mathematicaPath": "wolframscript",
|
||||
"mathematicaArgs": "-file",
|
||||
"mathematicaFileExtension": "wls",
|
||||
"mathematicaInject": "",
|
||||
"scalaPath": "scala",
|
||||
"scalaArgs": "",
|
||||
"scalaFileExtension": "scala",
|
||||
"scalaInject": "",
|
||||
"racketPath": "racket",
|
||||
"racketArgs": "",
|
||||
"racketFileExtension": "rkt",
|
||||
"racketInject": "#lang racket",
|
||||
"fsharpPath": "dotnet",
|
||||
"fsharpArgs": "",
|
||||
"fsharpInject": "",
|
||||
"fsharpFileExtension": "fsx",
|
||||
"cArgs": "",
|
||||
"cUseMain": true,
|
||||
"cInject": "",
|
||||
"rubyPath": "ruby",
|
||||
"rubyArgs": "",
|
||||
"rubyFileExtension": "rb",
|
||||
"rubyInject": "",
|
||||
"sqlPath": "psql",
|
||||
"sqlArgs": "-d <database> -U <user> -f",
|
||||
"sqlInject": "",
|
||||
"octavePath": "octave",
|
||||
"octaveArgs": "-q",
|
||||
"octaveFileExtension": "m",
|
||||
"octaveInject": "figure('visible','off') # Necessary to embed plots",
|
||||
"maximaPath": "maxima",
|
||||
"maximaArgs": "-qb",
|
||||
"maximaFileExtension": "mx",
|
||||
"maximaInject": "",
|
||||
"applescriptPath": "osascript",
|
||||
"applescriptArgs": "",
|
||||
"applescriptFileExtension": "scpt",
|
||||
"applescriptInject": "",
|
||||
"zigPath": "zig",
|
||||
"zigArgs": "run",
|
||||
"zigInject": "",
|
||||
"ocamlPath": "ocaml",
|
||||
"ocamlArgs": "",
|
||||
"ocamlInject": "",
|
||||
"jsInteractive": true,
|
||||
"tsInteractive": false,
|
||||
"csInteractive": false,
|
||||
"leanInteractive": false,
|
||||
"luaInteractive": false,
|
||||
"dartInteractive": false,
|
||||
"pythonInteractive": true,
|
||||
"cppInteractive": false,
|
||||
"prologInteractive": false,
|
||||
"shellInteractive": false,
|
||||
"batchInteractive": false,
|
||||
"bashInteractive": false,
|
||||
"groovyInteractive": false,
|
||||
"rInteractive": false,
|
||||
"goInteractive": false,
|
||||
"rustInteractive": false,
|
||||
"javaInteractive": false,
|
||||
"powershellInteractive": false,
|
||||
"kotlinInteractive": false,
|
||||
"swiftInteractive": false,
|
||||
"mathematicaInteractive": false,
|
||||
"haskellInteractive": false,
|
||||
"scalaInteractive": false,
|
||||
"fsharpInteractive": false,
|
||||
"cInteractive": false,
|
||||
"racketInteractive": false,
|
||||
"rubyInteractive": false,
|
||||
"sqlInteractive": false,
|
||||
"octaveInteractive": false,
|
||||
"maximaInteractive": false,
|
||||
"applescriptInteractive": false,
|
||||
"zigInteractive": false,
|
||||
"ocamlInteractive": false
|
||||
}
|
@ -74,53 +74,11 @@ Given the form $y = A\tan(Bx - C) + D$ (the same applies for $\cot$)
|
||||
- The range of both is $(-\infty, \infty)$
|
||||
- The phase shift is $\frac{C}{B}$
|
||||
- The vertical shift is $D$
|
||||
|
||||
# Secant
|
||||
$$ y = \sec(x) $$
|
||||

|
||||
|
||||
$$ sec(x) = \frac{1}{\cos{x}} $$
|
||||
Because secant is the reciprocal of cosine, when $\cos{x} = 0$, then secant is undefined. $|\cos$| 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.
|
||||
|
||||
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 function as they did to the sine and cosine functions.
|
||||
|
||||
# Cosecant
|
||||
$$ y = \csc(x) $$
|
||||

|
||||
|
||||
$$ \csc(x) = \frac{1}{\sin(x)} $$
|
||||
|
||||
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 sine crosses the x axis, an asymptote for a matching graph of cosecant will appear there.
|
||||
|
||||
The general form of cosecant is:
|
||||
$$ y = A\csc(B{x} - C) + D $$
|
||||
$A$, $B$, $C$, 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. (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 $x = \frac{C}{B} + \frac{\pi}{2} + \frac{\pi}{2} + \frac{\pi}{|B|}k$, 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: $\frac{2\pi}{\frac{\pi}{3}} = \frac{2\pi}{1} * \frac{3}{\pi} = 6$
|
||||
Phase shift: $\dfrac{\frac{\pi}{2}}{\frac{\pi}{3}} = \frac{3}{2}$
|
||||
Vertical shift: $1$
|
||||
|
||||
|
||||
| Transformation | Equation |
|
||||
| -------------- | ------------------------- |
|
||||
| Stretch | $\|-2\| = 2$ |
|
||||
|
Binary file not shown.
Before Width: | Height: | Size: 14 KiB |
Binary file not shown.
Before Width: | Height: | Size: 13 KiB |
Loading…
x
Reference in New Issue
Block a user