feat: inverse sin calculator in python

.gitignore

@@ -21,5 +21,5 @@ _deps
 bin
 ignored
 
-maths/*.pdf
-maths/*.synctex.gz
+maths/**/*.pdf
+maths/**/*.synctex.gz

.husky/scripts/cleanMaths.js

@@ -27,26 +27,40 @@ const cropBuffer = buffer =>
             .catch(err => reject(err));
     });
 
-fs.readdirSync(mathsDir).forEach(file => {
-    const [fileName, fileExtension] = file.split('.');
-    const filePath = path.join(mathsDir, file);
+const crawlDirectory = async dir => {
+    const dirents = fs.readdirSync(dir, { withFileTypes: true });
+
+    const files = await Promise.all(
+        dirents.map(dirent => {
+            const res = path.resolve(dir, dirent.name);
+            return dirent.isDirectory() ? crawlDirectory(res) : res;
+        })
+    );
+
+    return files.flat();
+};
+
+(async () => {
+    const files = await crawlDirectory(mathsDir);
+
+    files.forEach(file => {
+        const [filePath, fileDirectory, fileNameWithExt] = file.match(/(.*)\/((?:.(?!\/))+)$/);
+        const [fileName, fileExtension] = fileNameWithExt.split('.');
 
         if (file.endsWith('.pdf')) {
-        pdfToPng(filePath, {
-            viewportScale: 2
-        }).then(async output => {
+            pdfToPng(filePath).then(async output => {
                 const pageCount = output.length;
 
                 if (pageCount > 1)
                     output.forEach(async (page, i) =>
                         fs.writeFileSync(
-                        path.join(mathsDir, `${fileName}-${i + 1}.png`),
+                            path.join(fileDirectory, `${fileName}-${i + 1}.png`),
                             await cropBuffer(page.content)
                         )
                     );
                 else
                     fs.writeFileSync(
-                    path.join(mathsDir, `${fileName}.png`),
+                        path.join(fileDirectory, `${fileName}.png`),
                         await cropBuffer(output[0].content)
                     );
             });
@@ -56,3 +70,4 @@ fs.readdirSync(mathsDir).forEach(file => {
             fs.rmSync(filePath);
         }
     });
+})();

.vscode/settings.json

@@ -36,5 +36,5 @@
     },
     "latex-workshop.latex.autoBuild.run": "onSave",
     "latex-workshop.latex.autoClean.run": "onBuilt",
-    "latex-workshop.latex.search.rootFiles.include": ["**/*.tex", "root.tex"]
+    "latex-workshop.cls"
 }

languages/python/calculators/Trigometric Functions.py

@@ -1,19 +1,50 @@
-from cmath import e, sqrt
+from cmath import e, sqrt, log
 from _helpers import floatInput
 
 i = sqrt(-1)
 
 compute = lambda numerator, denominator: (numerator / denominator).real
+ln = lambda x: log(x, e)
+
 sin = lambda x: compute(pow(e, i * x) - pow(e, -i * x), 2 * i)
 cos = lambda x: compute(pow(e, i * x) + pow(e, -i * x), 2)
 tan = lambda x: compute(pow(e, i * x) - pow(e, -i * x), i * (pow(e, i * x) + pow(e, -i * x)))
+csc = lambda x: 1 / sin(x)
+sec = lambda x: 1 / cos(x)
+cot = lambda x: 1 / tan(x)
+
+arcsin = lambda x: (-i * ln((i * x) + sqrt(1 - pow(x, 2)))).real
+
+# todo: finish arc functions
+arccos = lambda x: None
+arctan = lambda x: None
+arccsc = lambda x: None
+arcsec = lambda x: None
+arccot = lambda x: None
+
 radians = floatInput("Please enter an amount of radians: ")
 
 print(f"""
-sin({radians}) = {sin(radians)})
+Trigometric functions
+
+sin({radians}) = {sin(radians)}
 cos({radians}) = {cos(radians)}
 tan({radians}) = {tan(radians)}
 
-csc({radians}) = {1 / sin(radians)}
-sec({radians}) = {1 / cos(radians)}
-cot({radians}) = {1 / tan(radians)}""")
+Reciprocal trigometric functions
+
+csc({radians}) = {csc(radians)}
+sec({radians}) = {sec(radians)}
+cot({radians}) = {cot(radians)}
+
+Inverse trigometric functions 
+
+arcsin({sin(radians)}) = {arcsin(sin(radians))}
+arccos({cos(radians)}) = {arccos(cos(radians))}
+arctan({tan(radians)}) = {arctan(tan(radians))}
+
+Inverse reciprocal trigometric functions
+
+arccsc({csc(radians)}) = {arccsc(csc(radians))}
+arcsec({sec(radians)}) = {arcsec(sec(radians))}
+arccot({cot(radians)}) = {arccot(cot(radians))}""")

maths/style.cls

@@ -1,3 +1,2 @@
-\ProvidesClass{style}
 \LoadClass[17pt]{extarticle}
 \pagenumbering{gobble}

maths/trigometric functions/sin.tex

@@ -0,0 +1,31 @@
+\documentclass{../style}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{gather*}
+	\text{By Euler's formula:} \\
+	e^{i\theta} = cos(\theta) + i\sin(\theta) \\
+	e^{-i\theta} = cos(\theta) - i\sin(\theta)
+\end{gather*}
+
+\begin{gather*}
+	\therefore \sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}
+\end{gather*}
+
+\begin{gather*}
+	\text{let} \quad \sin(\theta) = x \\
+	2ix = e^{i\theta} - e^{-i\theta} \\
+	2ie^{i\theta}x = (e^{i\theta})^2 - 1 \\ 
+	(e^{i\theta})^2 + (-2ix)e^{i\theta} - 1 = 0
+\end{gather*}
+
+\begin{gather*}
+	e^{i\theta} = \frac{-(-2ix) \pm \sqrt{(-2ix)^2 - 4(1)(-1)}}{2} = ix \pm \sqrt{1 - x^2} \\
+	i\theta = \ln(ix \pm \sqrt{1 - x^2}) \\
+	\theta = -i\ln(ix \pm \sqrt{1 - x^2})
+\end{gather*}
+
+\begin{gather*}
+	\therefore \arcsin(\theta) = -i\ln(i\theta \pm \sqrt{1 -\theta^2})
+\end{gather*}
+\end{document}

package.json

@@ -1,7 +1,8 @@
 {
     "name": "the-honk",
     "scripts": {
-        "prepare": "husky install"
+        "prepare": "husky install",
+        "maths": "node .husky/scripts/cleanMaths.js"
     },
     "devDependencies": {
         "@types/node": "^17.0.6",