From ad631f177d5d579fb152ee1e4aa25edcd7269343 Mon Sep 17 00:00:00 2001 From: newt Date: Wed, 9 Oct 2024 18:02:46 +0100 Subject: [PATCH] feat: finish arcus functions --- .husky/pre-commit | 1 + .../calculators/Trigometric Functions.py | 24 +++++++++------ maths/style.cls | 6 ++++ maths/trigometric functions/cos.png | Bin 0 -> 37370 bytes maths/trigometric functions/cos.tex | 27 ++++++++++++++++ maths/trigometric functions/cot-1.png | Bin 0 -> 25957 bytes maths/trigometric functions/cot-2.png | Bin 0 -> 26863 bytes maths/trigometric functions/cot.tex | 29 ++++++++++++++++++ maths/trigometric functions/csc-1.png | Bin 39604 -> 38988 bytes maths/trigometric functions/csc.tex | 8 ++--- maths/trigometric functions/sec-1.png | Bin 0 -> 39959 bytes maths/trigometric functions/sec-2.png | Bin 0 -> 4751 bytes maths/trigometric functions/sec.tex | 29 ++++++++++++++++++ maths/trigometric functions/sin.png | Bin 39788 -> 39318 bytes maths/trigometric functions/sin.tex | 10 ++---- maths/trigometric functions/tan-1.png | Bin 0 -> 20990 bytes maths/trigometric functions/tan-2.png | Bin 0 -> 26367 bytes maths/trigometric functions/tan.tex | 28 +++++++++++++++++ 18 files changed, 140 insertions(+), 22 deletions(-) create mode 100644 maths/trigometric functions/cos.png create mode 100644 maths/trigometric functions/cos.tex create mode 100644 maths/trigometric functions/cot-1.png create mode 100644 maths/trigometric functions/cot-2.png create mode 100644 maths/trigometric functions/cot.tex create mode 100644 maths/trigometric functions/sec-1.png create mode 100644 maths/trigometric functions/sec-2.png create mode 100644 maths/trigometric functions/sec.tex create mode 100644 maths/trigometric functions/tan-1.png create mode 100644 maths/trigometric functions/tan-2.png create mode 100644 maths/trigometric functions/tan.tex diff --git a/.husky/pre-commit b/.husky/pre-commit index 1ec3a16..d0a8bed 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -3,3 +3,4 @@ npx pretty-quick --staged node .husky/scripts/cleanMaths.js +git add . diff --git a/languages/python/calculators/Trigometric Functions.py b/languages/python/calculators/Trigometric Functions.py index 33eb62a..d0f39df 100644 --- a/languages/python/calculators/Trigometric Functions.py +++ b/languages/python/calculators/Trigometric Functions.py @@ -1,10 +1,10 @@ -from cmath import e, sqrt, log +from cmath import e, pi, sqrt, log from _helpers import floatInput i = sqrt(-1) compute = lambda numerator, denominator: (numerator / denominator).real -ln = lambda x: log(x, e) +computeInverse = lambda x: (-i * log(x, e)).real 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) @@ -13,14 +13,20 @@ 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 +arcsin = lambda x: computeInverse((i * x) + sqrt(1 - pow(x, 2))) +arccos = lambda x: computeInverse(x + sqrt(pow(x, 2) - 1)) +arctan = lambda x: computeInverse((i - x) / (i + x)) / 2 +arccsc = lambda x: computeInverse((pow(x, -1) * i) + sqrt(1 - pow(x, -2))) +arcsec = lambda x: computeInverse((pow(x, -1)) + sqrt(pow(x, -2) - 1)) +arccot = lambda x: computeInverse((x + i) / (x - i)) / 2 -# todo: finish arc functions -arccos = lambda x: None -arctan = lambda x: None -arccsc = lambda x: (-i * (ln((pow(x, -1) * i) + sqrt(1 - pow(x, -2))))).real -arcsec = lambda x: None -arccot = lambda x: None +# todo: hyperbolic functions + +# todo: hyperbolic inverse functions + +# todo: hyperbolic reciprocal functions + +# todo: hyperbolic inverse reciprocal functions radians = floatInput("Please enter an amount of radians: ") diff --git a/maths/style.cls b/maths/style.cls index 48621a0..0ae58c8 100644 --- a/maths/style.cls +++ b/maths/style.cls @@ -1,2 +1,8 @@ \LoadClass[17pt]{extarticle} \pagenumbering{gobble} + +\newcommand{\euler}{\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*}} diff --git a/maths/trigometric functions/cos.png b/maths/trigometric functions/cos.png new file mode 100644 index 0000000000000000000000000000000000000000..3aabec7c16b387bc6f25a5be607938f441be3754 GIT binary patch literal 37370 zcmeFac~sA9+xNfswj~K6$&`wygv=pRDr7848PXs^RHn)l4WyE(%tEP9ZDq`sp_vRR zB4ntPnFh1y_d0T2Yd!0Je#8I2_1tS+w~gxi8P4-K-qUf~Gl~b-4e7>~z+~RZ93taYY+dCt6Pxm=JQ?&J!_BJW^b5#sF zy3Wt&ieb&=rN8Fga=+EV+T(iimztwD>iktq6iYN!1Nfy;lqSCzsWj9IP)T2}tH>|S zOh@vIho+JVzcjGqi?lif`N_A8_&?wB`-yqGs&6*8u&_`uDc-N3_5N^5iqQbKq7gPW zYO^k^$hvv6X>|V8tdKUxrpBvv9vx`i^OwJN+w;ldY{)^&^76JXy8n zzWu7EGw#Gr=&Y|F%thW^(BEr8Y38Px=a&TXZPo8Dd~oXCtJfC$iz^)m?6W*(T|Dvr zKeGm{`fTvv!Gq$>)6XoZx;5m(*1dZzHn;14^mvmtJ(Je{TzM~X#>VN1*^eIW+ZecS zU;CvmZs`~rs%U8_D47&HFF4cg%=FC{xz>aJjhdgFf2ZsFozoM|qw^h3@Z-ksH`+FC zS5Hg3>4`fpl)ryJ@#&>C`LC80Z;BqhrDeNz!C5tV!zb}s-bJowrU!Vd>nc{QbM4oz zxVZT0_3LG8ujb~aNBPuL%$Ym4`cPI*PR-pZlRUdAD>Rs%sHT 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functions/csc.tex b/maths/trigometric functions/csc.tex index 1c43896..4a2c240 100644 --- a/maths/trigometric functions/csc.tex +++ b/maths/trigometric functions/csc.tex @@ -2,11 +2,7 @@ \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*} +\euler \begin{gather*} \therefore \sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i} \\ @@ -21,7 +17,7 @@ \end{gather*} \begin{gather*} - e^{i\theta} = \frac{-(\frac{2i}{x}) \pm \sqrt{(\frac{2i}{x})^2 - 4(1)(-1)}}{2} = x^{-1}i \pm \sqrt{1 - x^2} \\ + e^{i\theta} = \frac{-(\frac{2i}{x}) \pm \sqrt{(\frac{2i}{x})^2 - 4(-1)}}{2} = x^{-1}i \pm \sqrt{1 - x^2} \\ i\theta = \ln(x^{-1}i \pm \sqrt{1 - x^2}) \\ \theta = -i\ln(x^{-1}i \pm \sqrt{1 - x^2}) \end{gather*} diff --git a/maths/trigometric functions/sec-1.png b/maths/trigometric functions/sec-1.png new file mode 100644 index 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