{"id":202182,"date":"2018-08-15T22:01:48","date_gmt":"2018-08-15T15:01:48","guid":{"rendered":"https:\/\/www.quipper.com\/id\/blog\/?p=202182"},"modified":"2022-03-01T17:06:39","modified_gmt":"2022-03-01T10:06:39","slug":"rumus-identitas-trigonometri","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/rumus-identitas-trigonometri\/","title":{"rendered":"Menghitung Tinggi Pohon Menggunakan Rumus Identitas Trigonometri"},"content":{"rendered":"

\"\"<\/a><\/p>\n

Tahukah kamu, Quipperian, trigonometri adalah salah satu topik dalam matematika yang membahas mengenai hubungan antara sisi dan sudut pada segitiga? <\/span>Trigonometri digunakan di seluruh konsep geometri (gambar, ukuran, dan bentuk bangun bidang maupun ruang) karena setiap bentuk geometri yang seluruh sisinya lurus selalu dapat dipecah menjadi kumpulan segitiga. Selain itu, bisa dibilang bahwa trigonometri juga menjadi dasar bagi topik matematika lainnya seperti bilangan kompleks, deret tak terbatas, logaritma, dan kalkulus, <\/span>lho<\/span><\/em>. Keren, ya!<\/span><\/p>\n

Kata trigonometri itu sendiri merupakan turunan dari Bahasa Latin pada abad ke enam belas dari Bangsa Yunani, yaitu <\/span>trigonnon<\/span><\/em> yang berarti segitiga dan <\/span>metron<\/span><\/em> yang berarti ukuran. Meskipun teori mengenai trigonometri telah muncul di Yunani sejak abad ke-tiga sebelum masehi, beberapa kontribusi yang paling penting (seperti fungsi sinus) justru datang dari India pada abad ke-lima masehi. <\/span><\/p>\n

Karena jejak ilmu pengetahuan Bangsa Yunani kuno mengenai trigonometri telah hilang, tidak diketahui secara pasti apakah para cendekiawan Bangsa India mengembangkan ilmu tersebut secara mandiri atau mengikuti pengaruh Bangsa Yunani. Menurut Victor Katz, seorang ahli matematika asal Philadelphia, dalam bukunya yang berjudul \u201c<\/span>A History of Mathematics<\/span><\/em>\u201d, trigonometri dikembangkan terutama karena kebutuhan para astronom Yunani dan India.<\/span><\/p>\n

1. Sinus, Kosinus, dan Tangen<\/strong><\/h2>\n

\"\"<\/a><\/p>\n

Segitiga yang digunakan pada konsep trigonometri adalah segitiga siku-siku. Dalam menyelesaikan soal trigonometri, rumus apa yang perlu digunakan sangat bergantung pada kombinasi sisi dan sudut yang diketahui. <\/span><\/p>\n

Juga terdapat dua fungsi trigonometri dasar yang sangat fundamental, yaitu fungsi sinus (ditulis sebagai sin(\u03b1)), fungsi kosinus (ditulis sebagai cos(\u03b1)), dan juga fungsi tangen (ditulis sebagai tan(\u03b1)), dengan \u03b1 merupakan salah satu sudut segitiga siku-siku.<\/span><\/p>\n

\"\"<\/a><\/p>\n

Sebelum berlanjut ke identitas trigonometri lebih jauh, ada beberapa definisi yang Quipperian perlu ketahui, nih! Jika kita memiliki suatu segitiga siku-siku ABC dengan salah satu sudut sebesar \u03b1 seperti pada gambar di atas maka sisi yang berada di seberang sudut \u03b1 disebut juga sebagai sisi depan, sisi tegak yang berada di dekat sudut \u03b1 sebagai sisi samping, dan sisanya menjadi sisi miring.<\/span><\/p>\n

Nah selanjutnya, fungsi dasar dalam trigonometri didefinisikan sebagai berikut:<\/span><\/p>\n

    \n
  1. Sin(\u03b1) merupakan panjang sisi depan dibagi sisi miring atau biasa disingkat menjadi \u201cDemi\u201d (depan per miring).<\/span><\/li>\n
  2. Cos(\u03b1) merupakan panjang sisi samping dibagi sisi miring atau biasa disingkat menjadi \u201cSami\u201d (samping per miring).<\/span><\/li>\n
  3. Tan(\u03b1) merupakan panjang sisi depan dibagi sisi samping atau biasa disingkat menjadi \u201cDesa\u201d (depan per samping).<\/span><\/li>\n<\/ol>\n

    Dengan demikian, untuk mengingat tiga rumus dasar trigonometri di atas, Quipperian cukup menghafalkan Demi Sami Desa saja. Mudah, kan?<\/span><\/p>\n

    2. Identitas Trigonometri Lainnya<\/strong><\/h2>\n

    \"\"<\/a><\/p>\n

    Tiga rumus dasar trigonometri yang telah kita bahas di atas dapat dikembangkan menjadi rumus identitas trigonometri lainnya, Quipperian! Berikut pembahasannya:<\/span><\/p>\n

    a. Identitas Kebalikan<\/strong><\/h3>\n

    Fungsi sinus, kosinus, dan tangen memiliki fungsi kebalikan terhadap perkalian, yaitu sebagai berikut:<\/span><\/p>\n

    1) Fungsi sinus berkebalikan dengan fungsi kosekan (coses(<\/span>\u03b1<\/span>))<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    2) Fungsi kosinus berkebalikan dengan fungsi sekan (sec(\u03b1))<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    3) Fungsi tangen berkebalikan dengan fungsi kotangen (cot(\u03b1))<\/span><\/p>\n

    b. Identitas Phytagoras<\/em><\/strong><\/h3>\n

    \"\"<\/a><\/p>\n

    Berdasarkan rumus <\/span>phytagoras<\/span><\/em>, akan diperoleh rumus identitas lainnya dari fungsi-fungsi trigonometri seperti pada penjelasan berikut:<\/span><\/p>\n

    1) Menggunakan segitiga pada poin 1 dan rumus <\/span>phytagoras<\/span><\/em>, diperoleh:<\/span><\/p>\n

    BC<\/span>2<\/span><\/sup> + AC2 = AB<\/span>2<\/span><\/sup><\/p>\n

    2) Dari rumus sinus dan kosinus pada poin 1, diperoleh:<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    3) Substitusikan dua persamaan pada poin 2) ke dalam persamaan pada poin 1), diperoleh:<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    Contoh Soal:<\/span><\/p>\n

    Dengan menggunakan rumus identitas kebalikan dan <\/span>phytagoras<\/span><\/em>, buktikan bahwa<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    Jawab:<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    3. Aplikasi Trigonometri dalam Kehidupan Sehari-Hari<\/strong><\/h2>\n

    \"\"<\/a><\/p>\n

    Jika suatu hari Quipperian sedang berdiri di hadapan sebuah pohon, kamu bisa mengukur tinggi pohon tersebut tanpa menggunakan meteran, <\/span>lho<\/span><\/em>! Yang perlu kamu ketahui cukup tinggi badan kamu, jarak antara kamu dan pohon, serta sudut elevasi antara mata kamu dengan puncak pohon. Sudut elevasi adalah sudut yang terbentuk antara garis lurus mendatar dengan garis Quipperian ke atas.<\/span><\/p>\n

    Contoh Soal:<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    Jawab:<\/span><\/p>\n

    Berdasarkan rumus tangen:<\/span><\/p>\n

    \"\"<\/a><\/p>\n

    Diperoleh tinggi pohon = tinggi pohon dari pucuk hingga setara mata siswa + tinggi siswa<\/span><\/p>\n

    = 4 + 1,6 = 5,6 m<\/span><\/p>\n

    Nah, jika Quipperian ingin mengetahui lebih dalam tentang rumus identitas trigonometri atau rumus lain beserta aplikasinya, kamu bisa mempelajarinya pada bidang Matematika melalui Quipper Video! Yuk, berlangganan dengan klik link di bawah ini! Selamat memahami konsep matematika di sekitar kita, Quipperian!<\/span><\/p>\n

    Link cara daftar: <\/span>bit.ly\/caradaftarquipper<\/span><\/a><\/p>\n

    Link registrasi: <\/span>https:\/\/learn.quipper.com\/signup\/video\/ID<\/span><\/a><\/p>\n

     <\/p>\n

    Penulis: Laili Miftahur Rizqi<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

    Tahukah kamu, Quipperian, trigonometri adalah salah satu topik dalam matematika yang membahas mengenai hubungan antara sisi dan sudut pada segitiga? Trigonometri digunakan di seluruh…<\/p>\n","protected":false},"author":99400369,"featured_media":202222,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384888,679384865],"tags":[],"ppma_author":[679386827],"class_list":["post-202182","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika"],"acf":[],"yoast_head":"\nMenghitung Tinggi Pohon Menggunakan Rumus Identitas Trigonometri<\/title>\n<meta name=\"description\" content=\"Pernah enggak sih kamu pingin tahu tinggi pohon dibandingkan tinggimu sendiri? 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