{"id":214,"date":"2023-07-11T15:40:45","date_gmt":"2023-07-11T15:40:45","guid":{"rendered":"https:\/\/mathority.org\/id\/sistem-koordinat-bola-silinder-kutub-kartesius\/"},"modified":"2023-07-11T15:40:45","modified_gmt":"2023-07-11T15:40:45","slug":"sistem-koordinat-bola-silinder-kutub-kartesius","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/sistem-koordinat-bola-silinder-kutub-kartesius\/","title":{"rendered":"Sistem koordinasi"},"content":{"rendered":"<p>Di halaman ini kami menjelaskan apa itu sistem koordinat dan, sebagai tambahan, Anda akan menemukan segala sesuatu tentang sistem koordinat Cartesian. Anda juga akan melihat jenis sistem koordinat lainnya (kutub, silinder, bola, dll.) dan penerapan sistem koordinat di dunia nyata. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-sistema-de-coordenadas\"><\/span> Apa itu sistem koordinat?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Walaupun pada awalnya agak sulit untuk memahami konsep ini, namun pengertian sistem koordinat adalah:<\/p>\n<p> <strong>Sistem koordinat<\/strong> adalah sistem yang memungkinkan kita mengidentifikasi posisi suatu titik. Artinya, ini adalah sekumpulan nilai yang digunakan untuk menentukan lokasi objek geometris apa pun.<\/p>\n<p> Misalnya, posisi terbang pesawat berikut dapat digambarkan dengan sistem koordinat: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quest-ce-quun-systeme-de-coordonnees.webp\" alt=\"apa itu sistem koordinat\" class=\"wp-image-658\" width=\"348\" height=\"346\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Dalam hal ini, bidang berada di titik (5.3). Karena koordinat X-nya 5 dan koordinat Y-nya 3.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6042f2d3f2552672e37a208d8f141b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(5,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebaliknya titik (0,0) disebut titik <strong>asal koordinat<\/strong> , karena merupakan titik awal sumbu koordinat dan merupakan titik acuan sistem koordinat.<\/p>\n<p> Karena penasaran, ahli matematika yang menemukan sistem koordinat dianggap sebagai orang Prancis Ren\u00e9 Descartes. Oleh karena itu disebut juga sistem koordinat kartesius. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"sistema-de-coordenadas-cartesianas-en-el-plano\"><\/span> Sistem koordinat kartesius pada bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Grafik yang kita lihat pada bagian sebelumnya termasuk dalam sistem koordinat kartesius pada bidang. Kita katakan ia berada pada bidang karena merupakan sistem dua dimensi, artinya ia hanya mempunyai dua sumbu: sumbu X dan sumbu Y.<\/p>\n<p> Sumbu X mewakili koordinat horizontal, sedangkan sumbu Y mewakili koordinat vertikal. Di bawah ini Anda dapat melihat beberapa titik yang direpresentasikan secara grafis beserta koordinatnya: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/systeme-de-coordonnees-cartesiennes-du-plan.webp\" alt=\"Sistem koordinat kartesius pada bidang\" class=\"wp-image-664\" width=\"401\" height=\"362\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Seperti terlihat pada grafik, koordinat direpresentasikan secara numerik dengan tanda kurung, selain itu komponen X didahulukan baru kemudian komponen Y: (4,3). Selain itu, koordinat bisa positif, negatif, atau nol.<\/p>\n<p> Di sisi lain, sistem koordinat jenis ini disebut juga bidang kartesius.<\/p>\n<p> Terakhir, Anda harus tahu bahwa sumbu koordinat dapat dinyatakan dalam beberapa cara, meskipun semuanya memiliki arti yang sama:<\/p>\n<ul>\n<li> Sumbu X disebut juga sumbu absis atau sumbu OX.<\/li>\n<li> Sumbu Y disebut juga sumbu y atau sumbu OY. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"sistema-de-coordenadas-cartesianas-en-el-espacio\"><\/span> Sistem koordinat kartesius di ruang angkasa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita baru saja melihat bagaimana merepresentasikan suatu titik pada bidang, yaitu dalam sistem koordinat dengan dua sumbu (2 dimensi). Namun kenyataannya terdiri dari 3 dimensi (tinggi, lebar dan kedalaman).<\/p>\n<p> Jadi, dalam geometri Euclidean, ruang tiga dimensi umumnya diwakili oleh sistem koordinat dengan tiga sumbu, semuanya tegak lurus satu sama lain:<\/p>\n<ul>\n<li> Sumbu X mewakili kedalaman.<\/li>\n<li> Sumbu Y menunjukkan lebarnya.<\/li>\n<li> Sumbu Z berhubungan dengan ketinggian. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/systeme-de-coordonnees-cartesiennes-dans-lespace.webp\" alt=\"Sistem koordinat kartesius dalam ruang 3D\" class=\"wp-image-669\" width=\"396\" height=\"419\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Seperti yang Anda lihat pada representasi grafis sebelumnya, koordinat titik mana pun diberikan oleh proyeksi pada sumbu jarak antara titik tersebut dan titik asal (0,0,0). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"sistema-de-coordenadas-polares\"><\/span> sistem koordinat kutub<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sistem koordinat kartesius, 2D atau 3D, adalah yang paling banyak digunakan. Namun pada beberapa kesempatan mungkin lebih mudah bagi kita untuk menggunakan sistem koordinat jenis lain.<\/p>\n<p> <strong>Sistem koordinat kutub<\/strong> merupakan sistem acuan dua dimensi yang koordinatnya adalah:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bbd3dad8e9bf4fcf503ee96529d6e22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah jarak antara titik asal koordinat dan titik. Ini disebut koordinat radial.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-312a5a92e31e6e39fb0a2a2f56daa6b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sudut yang dibuat sumbu X dengan garis yang melalui titik dan titik asal. Ini disebut koordinat sudut atau azimut. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/systemes-de-coordonnees-polaires.webp\" alt=\"sistem koordinat kutub\" class=\"wp-image-679\" width=\"227\" height=\"236\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Anda dapat dengan mudah beralih dari sistem koordinat persegi panjang ke sistem koordinat kutub menggunakan persamaan berikut: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-197\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Ubah koordinat kutub menjadi koordinat kartesius<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c979a6df1dcce26d502f711cec3bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=r\\cdot\\text{cos}(\\theta)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58c4d1f255bf1b333f5ea096c56cd073_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=r\\cdot\\text{sen}(\\theta)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Peralihan dari koordinat Kartesius ke koordinat kutub<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21d7af3356d5313378cc53ac2ddccb15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r= \\sqrt{x^2+y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3b6050a358df0d194ba6e0341a7d3e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\theta = \\text{arctan}\\left(\\frac{y}{x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"117\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"sistema-de-coordenadas-cilindricas\"><\/span> Sistem koordinat silinder<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sistem koordinat silinder sangat mirip dengan sistem koordinat kutub. Sebenarnya sama saja tetapi dengan satu koordinat lagi: tinggi.<\/p>\n<p> Oleh karena itu, <strong>bingkai silinder<\/strong> adalah bingkai tiga dimensi, yaitu dengan 3 koordinat:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bbd3dad8e9bf4fcf503ee96529d6e22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah proyeksi ortogonal titik pada bidang XY, atau dengan kata lain jarak titik terhadap sumbu Z.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-312a5a92e31e6e39fb0a2a2f56daa6b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sudut sumbu semi positif<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-552b9c264efd969e3ec2d40c6863744a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{z}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah ketinggian titik, sama dengan koordinat sistem koordinat Kartesius di ruang angkasa. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/systeme-de-coordonnees-cylindrique.webp\" alt=\"sistem koordinat silinder\" class=\"wp-image-692\" width=\"304\" height=\"316\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Rumus berikut digunakan untuk mengubah sistem koordinat kartesius menjadi koordinat silinder: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-200\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Ubah koordinat silinder menjadi koordinat kartesius<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c979a6df1dcce26d502f711cec3bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=r\\cdot\\text{cos}(\\theta)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-58c4d1f255bf1b333f5ea096c56cd073_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=r\\cdot\\text{sen}(\\theta)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccad145365777ca8f135037fffb943db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z = z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Ubah koordinat kartesius menjadi koordinat silinder<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21d7af3356d5313378cc53ac2ddccb15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r= \\sqrt{x^2+y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3b6050a358df0d194ba6e0341a7d3e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\theta = \\text{arctan}\\left(\\frac{y}{x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"117\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccad145365777ca8f135037fffb943db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z = z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"sistema-de-coordenadas-esfericas\"><\/span> Sistem koordinat bola<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Terakhir, kita memiliki sistem koordinat bola. Sistem koordinat jenis ini juga sangat mirip dengan koordinat kutub dan koordinat silinder, meskipun jelas terdapat beberapa perbedaan dari keduanya.<\/p>\n<p> <strong>Sistem koordinat bola<\/strong> merupakan suatu sistem untuk menggambarkan ruang Euclidean tiga dimensi, oleh karena itu mempunyai tiga koordinat:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bbd3dad8e9bf4fcf503ee96529d6e22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah jarak (dalam R3) dari titik asal ke titik.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-312a5a92e31e6e39fb0a2a2f56daa6b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sudut yang dibentuk bagian positif sumbu X terhadap garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> diproyeksikan ke bidang XY.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d025a4c6fa30260228557b9899b6ed95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\phi}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah sudut antara bagian positif sumbu Z dan garis <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/systeme-de-coordonnees-spheriques.webp\" alt=\"sistem koordinat bola\" class=\"wp-image-698\" width=\"321\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Anda dapat beralih antara koordinat bola dan kartesius menggunakan rumus berikut: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-203\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Mengubah koordinat bola menjadi koordinat kartesius<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e77b37ce6c4d5efc6f0ac34e0c6d1cd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=r\\cdot\\text{cos}(\\theta)\\cdot\\text{sen}(\\phi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-219ca466e17404eda7a11f1955277863_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=r\\cdot \\text{sen}(\\theta)\\cdot\\text{sen}(\\phi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35ab46e7ae38282021bdccc29cfd6d22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z = r\\cdot\\text{cos}(\\phi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff6f00\"> <strong>Mengubah koordinat kartesius menjadi koordinat bola<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94148711df57a647d357b081e42e05a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r= \\sqrt{x^2+y^2+z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"145\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3b6050a358df0d194ba6e0341a7d3e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\theta = \\text{arctan}\\left(\\frac{y}{x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"117\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e170d40bec9371824b72ef026c7c6d87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\phi = \\text{arctan}\\left(\\frac{\\sqrt{x^2+y^2}}{z}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"189\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-reales-del-sistema-de-coordenadas\"><\/span> Aplikasi sistem koordinat di dunia nyata<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sistem koordinat sangat penting dalam matematika karena juga digunakan dalam kehidupan nyata. Misalnya, berguna untuk menemukan lokasi objek, orang, atau bahkan tempat di peta. Faktanya, GPS ada karena sistem koordinat, karena itulah yang digunakan untuk mengetahui posisi Anda di Bumi.<\/p>\n<p> Lebih tepatnya, koordinat geografis GPS terdiri dari dua elemen: lintang dan bujur. Lintang (utara atau selatan) dan bujur (timur atau barat) adalah dua koordinat sudut yang mengukur sudut antara pusat bumi dan lokasi Anda. Keduanya dinyatakan dalam derajat, baik dalam koordinat desimal maupun sexagesimal.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini kami menjelaskan apa itu sistem koordinat dan, sebagai tambahan, Anda akan menemukan segala sesuatu tentang sistem koordinat Cartesian. Anda juga akan melihat jenis sistem koordinat lainnya (kutub, silinder, bola, dll.) dan penerapan sistem koordinat di dunia nyata. Apa itu sistem koordinat? Walaupun pada awalnya agak sulit untuk memahami konsep ini, namun pengertian &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/sistem-koordinat-bola-silinder-kutub-kartesius\/\"> <span class=\"screen-reader-text\">Sistem koordinasi<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[47],"tags":[],"class_list":["post-214","post","type-post","status-publish","format-standard","hentry","category-titik-garis-dan-bidang"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sistem koordinat - Mathoritas<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/sistem-koordinat-bola-silinder-kutub-kartesius\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sistem koordinat - Mathoritas\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini kami menjelaskan apa itu sistem koordinat dan, sebagai tambahan, Anda akan menemukan segala sesuatu tentang sistem koordinat Cartesian. Anda juga akan melihat jenis sistem koordinat lainnya (kutub, silinder, bola, dll.) dan penerapan sistem koordinat di dunia nyata. Apa itu sistem koordinat? 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