{"id":312789,"date":"2023-05-22T09:37:23","date_gmt":"2023-05-22T02:37:23","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=312789"},"modified":"2023-05-22T09:37:33","modified_gmt":"2023-05-22T02:37:33","slug":"tabel-trigonometri","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/tabel-trigonometri\/","title":{"rendered":"Tabel Trigonometri Berdasarkan Kuadran dan Sudut Istimewa"},"content":{"rendered":"\n
\"Tabel<\/figure>\n\n\n\n

Hai Quipperian, di artikel sebelumnya Quipper Blog sudah pernah membahas konsep dasar trigonometri. Saat belajar trigonometri, pasti kamu akan bertemu dengan sudut istimewa, kan? Sudut istimewa sendiri dimulai dari 0o dan berakhir di 360o. Apakah kamu sudah hafal nilai trigonometri <\/a>untuk sudut-sudut tersebut? Tentu tidak mudah menghafalkan semuanya, ya. Untuk memudahkanmu, kali ini Quipper Blog akan membahas tentang tabel trigonometri. Bagaimana bentuk tabel trigonometri itu? Yuk, simak selengkapnya!<\/p>\n\n\n\n

Pengertian Tabel Trigonometri<\/h2>\n\n\n\n

Tabel trigonometri adalah tabel yang berisi nilai trigonometri sudut-sudut istimewa<\/strong>. Sudut istimewa adalah sudut yang memiliki nilai trigonometri mudah untuk diingat dan dihafalkan. Oleh karena sudut memiliki rentang antara 0o<\/sup> sampai 360o<\/sup>, maka ada sifat pengulangan untuk sudut-sudut istimewa, misalnya nilai sin 30o<\/sup> = sin 150o<\/sup> = 0,5.<\/p>\n\n\n\n

Nilai Trigonometri Berdasarkan Kuadran<\/h2>\n\n\n\n

Nilai trigonometri suatu sudut bergantung pada letak kuadrannya. Kuadran sudut dibagi menjadi empat, yaitu kuadran I, kuadran II, kuadran III, dan kuadran IV. Lalu, apa perbedaan kuadran-kuadran tersebut?<\/p>\n\n\n\n

Kuadran I<\/h3>\n\n\n\n

Kuadran I terletak di antara sudut 0o<\/sup> sampai 90o<\/sup>. Di kuadran ini, semua nilai trigonometri akan bernilai positif, baik sinus \u03b1, cosinus \u03b1, maupun tangen \u03b1.<\/p>\n\n\n\n

Kuadran II<\/h3>\n\n\n\n

Kuadran II terletak di antara sudut 90o<\/sup> sampai 180o<\/sup>. Di kuadran ini, hanya sinus \u03b1 yang akan bernilai positif. Untuk cosinus \u03b1 dan tangen \u03b1 akan bernilai negatif. Contoh, sin 120o<\/sup>=1\/2\u221a3 = 1\/2 dan cos 120o<\/sup>=-1\/2<\/p>\n\n\n\n

Kuadran III<\/h3>\n\n\n\n

Kuadran III terletak di antara sudut 180o<\/sup> sampai 270o<\/sup>. Di kuadran ini, hanya tangen \u03b1 yang bernilai positif. Sementara cosinus \u03b1 dan sinus \u03b1 akan bernilai negatif.<\/p>\n\n\n\n

Kuadran IV<\/h3>\n\n\n\n

Kuadran IV terletak di antara sudut 270o<\/sup> sampai 360o<\/sup>. Di kuadran ini, hanya cosinus \u03b1 yang bernilai positif. Sementara sinus \u03b1 dan tan \u03b1 akan bernilai negatif.<\/p>\n\n\n\n

Untuk lebih jelasnya, perhatikan letak kuadran berikut ini.<\/p>\n\n\n\n

\"perhatikan<\/figure>\n\n\n\n

Agar lebih mudah dalam mengingat nilai trigonometrinya, gunakan SUPER \u201cSolusi Quipper\u201d berikut.<\/p>\n\n\n\n

\u201cSEMUA SINDIKAT TANGANNYA KOSONG\u201d<\/p>\n\n\n\n

Artinya: di kuadran I semua<\/strong> bernilai positif, di kuadran II hanya sin<\/strong> yang positif, di kuadran III hanya tan<\/strong> yang positif, dan di kuadran IV hanya cos<\/strong> yang positif.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Tabel Trigonometri Sudut Istimewa Lengkap<\/h2>\n\n\n\n

Mungkin kamu biasa mengenal sudut istimewa 0o<\/sup> sampai 90o<\/sup>. Tahukah kamu jika sudut istimewa itu tidak hanya terbatas sampai 90o<\/sup>, namun sampai 360o<\/sup>. Berikut ini akan disajikan tabel trigonometri sudut istimewa lengkap mulai 0o<\/sup> sampai 360o<\/sup>.<\/p>\n\n\n\n

Tabel Trigonometri di Kuadran I (0o<\/sup> \u2013 90o<\/sup>)<\/h3>\n\n\n\n

Sudut istimewa yang berada di kuadran I meliputi, 0o<\/sup>, 30o<\/sup>, 45o<\/sup>, 60o<\/sup>, dan 90o<\/sup>. Adapun tabel trigonometri sudut istimewa di kuadran I adalah sebagai berikut.<\/p>\n\n\n\n

\"Tabel<\/figure>\n\n\n\n

Tabel Trigonometri di Kuadran II (90o<\/sup> \u2013 180o<\/sup>)<\/h3>\n\n\n\n

Sudut istimewa yang berada di kuadran II meliputi 90o<\/sup>, 120o<\/sup>, 135o<\/sup>, 150o<\/sup>, dan 180o<\/sup>. Adapun tabel trigonometri sudut istimewa di kuadran II adalah sebagai berikut.<\/p>\n\n\n\n

\"Tabel<\/figure>\n\n\n\n

Tabel Trigonometri di Kuadran III (180o<\/sup> \u2013 270o<\/sup>)<\/h3>\n\n\n\n

Sudut istimewa yang berada di kuadran II meliputi 180o<\/sup>, 210o<\/sup>, 225o<\/sup>, 240o<\/sup>, dan 270o<\/sup>. Adapun tabel trigonometri sudut istimewa di kuadran III adalah sebagai berikut.<\/p>\n\n\n\n

\"Tabel<\/figure>\n\n\n\n

Tabel Trigonometri di Kuadran IV (270o<\/sup> \u2013 360o<\/sup>)<\/h3>\n\n\n\n

Sudut istimewa yang berada di kuadran II meliputi 270o<\/sup>, 300o<\/sup>, 315o<\/sup>, 330o<\/sup>, dan 360o<\/sup>. Adapun tabel trigonometri sudut istimewa di kuadran IV adalah sebagai berikut.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\n

Baca Juga: <\/span> Rumus Perbandingan Trigonometri, Sudut Istimewa pada Segitiga Siku Siku<\/a><\/p>\n<\/div>\n\n\n\n

Persamaan Nilai Trigonometri Antar Kuadran<\/h2>\n\n\n\n

Dari tabel di atas, bisa disimpulkan bahwa sudut-sudut di setiap kuadran ada yang memiliki nilai trigonometri sama, misalnya sin 210o<\/sup> = sin 330o<\/sup> = -0,5, cos = 120o<\/sup> = cos 240o<\/sup> = -0,5. Dari kesamaan nilai-nilai tersebut, diperoleh suatu persamaan yang bisa memudahkanmu dalam menyelesaikan nilai trigonometri antarkuadran. Berikut ini persamaannya.<\/p>\n\n\n\n

Persamaan Trigonometri di Kuadran I (0o<\/sup> \u2013 90o<\/sup>)<\/h3>\n\n\n\n

Adapun persamaan yang berlaku pada trigonometri di kuadran I adalah sebagai berikut.<\/p>\n\n\n\n

    \n
  1. sin(90o<\/sup> \u2013 \u03b1) = cos\u03b1<\/li>\n\n\n\n
  2. cos(90o<\/sup> \u2013 \u03b1) = sin\u03b1<\/li>\n\n\n\n
  3. tan(90o<\/sup> \u2013 \u03b1) = cot\u03b1<\/li>\n<\/ol>\n\n\n\n

    Perhatikan contoh berikut.<\/p>\n\n\n\n

    Buktikan bahwa nilai dari sin(90 \u2013 30o<\/sup>) = cos(30o<\/sup>)<\/p>\n\n\n\n

    Pembahasan :<\/p>\n\n\n\n

    Dari persamaan sin(90o<\/sup> \u2013 \u03b1) = -cos\u03b1, diperoleh :<\/p>\n\n\n\n

    sin(90 \u2013 30o<\/sup>) = cos(30o<\/sup>)<\/p>\n\n\n\n

    \u2194 sin 60o<\/sup> = cos 30o<\/sup><\/p>\n\n\n\n

    Untuk membuktikannya, lihat kembali tabel trigonometri!<\/p>\n\n\n\n

    \"Persamaan<\/figure>\n\n\n\n

    Coba kamu perhatikan sel yang diberi warna ungu. Dari situ, terlihat jika nilai sin(60o<\/sup>)<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Persamaan Trigonometri di Kuadran II (90o<\/sup> \u2013 180o<\/sup>)<\/h3>\n\n\n\n

    Berdasarkan tabel, diperoleh hubungan bahwa sin(120o<\/sup>) = sin(60o<\/sup>), di mana 120o<\/sup> + 60o<\/sup> = 180o<\/sup>. Dengan demikian, persamaan yang berlaku adalah sebagai berikut.<\/p>\n\n\n\n

      \n
    1. sin(180o<\/sup> \u2013 \u03b1) = sin\u03b1<\/li>\n\n\n\n
    2. cos(180o<\/sup> \u2013 \u03b1) = -cos\u03b1<\/li>\n\n\n\n
    3. tan(180o<\/sup> \u2013 \u03b1) = -tan\u03b1<\/li>\n<\/ol>\n\n\n\n

      Perhatikan contoh berikut.<\/p>\n\n\n\n

      Buktikan bahwa cos(180o<\/sup> \u2013 45o<\/sup>) = -cos(45o<\/sup>)<\/p>\n\n\n\n

      Pembahasan :<\/p>\n\n\n\n

      cos(180o<\/sup> \u2013 45o<\/sup>) = -cos(45o<\/sup>)<\/p>\n\n\n\n

      \u2194 cos(135o<\/sup>) = -cos(45o<\/sup>)<\/p>\n\n\n\n

      \u2194 – 1\/2\u221a2 = -1\/2 \u221a2 (terbukti)<\/p>\n\n\n\n

      Persamaan Trigonometri di Kuadran III (180o<\/sup> \u2013 270o<\/sup>)<\/h3>\n\n\n\n

      Adapun persamaan trigonometri di kuadran III adalah sebagai berikut.<\/p>\n\n\n\n

        \n
      1. sin(180o<\/sup> + \u03b1) = -sin\u03b1<\/li>\n\n\n\n
      2. cos(180o<\/sup> + \u03b1) = -cos\u03b1<\/li>\n\n\n\n
      3. tan(180o<\/sup> + \u03b1) = tan\u03b1<\/li>\n<\/ol>\n\n\n\n

        Persamaan Trigonometri di Kuadran IV (180o<\/sup> \u2013 270o<\/sup>)<\/h3>\n\n\n\n

        Untuk di kuadran IV, berlaku persamaan trigonometri sudut negatif sebagai berikut.<\/p>\n\n\n\n

          \n
        1. sin (360o<\/sup> – \u03b1) = -sin \u03b1<\/li>\n\n\n\n
        2. cos (360o<\/sup> – \u03b1) = cos \u03b1<\/li>\n\n\n\n
        3. tan (360o<\/sup> – \u03b1) = -tan \u03b1<\/li>\n<\/ol>\n\n\n\n

          Mengapa sudutnya negatif? Karena sudut negatif diukur dari sumbu-x positif yang arahnya searah dengan putaran jarum jam.<\/p>\n\n\n\n

          Dengan adanya persamaan-persamaan di atas, kamu tidak perlu repot-repot menghafalkan semua nilai trigonometri mulai 0o sampai 360o, ya. Cukup pahami rumus dan letak kuadran sudutnya.<\/p>\n\n\n\n

          \n

          Baca Juga: <\/span> Rumus Identitas Trigonometri, Contoh Soal dan Pembahasannya<\/a><\/p>\n<\/div>\n\n\n\n

          Contoh Soal<\/h2>\n\n\n\n

          Untuk mengasah kemampuanmu, yuk simak contoh soal berikut ini.<\/p>\n\n\n\n

          Contoh Soal 1<\/h3>\n\n\n\n

          Jika sinx = sin(60o<\/sup>) dengan 0o<\/sup> \u2264 x \u2264 360o<\/sup>, tentukan sudut x yang memenuhi persamaan tersebut!<\/p>\n\n\n\n

          Pembahasan :<\/p>\n\n\n\n

          Di soal tertulis bahwa sinx = sin(60o<\/sup>) dengan 0o<\/sup> \u2264 x \u2264 360o<\/sup>. Artinya, solusi untuk sudut x hanya berada di kuadran I dan kuadran II. Mengapa demikian? Karena sinus bernilai positif di kuadran II. Dengan demikian, diperoleh dua solusi seperti berikut.<\/p>\n\n\n\n

            \n
          1. sinx = sin(60o<\/sup>) \u2192 x = 60o<\/sup><\/li>\n\n\n\n
          2. sin(180o<\/sup> \u2013 60o<\/sup>) = sin(60o<\/sup>) \u2192 x = 120o<\/sup><\/li>\n<\/ol>\n\n\n\n

            Jadi, nilai sudut x yang memenuhi adalah {60o<\/sup>, 120o<\/sup>}.<\/p>\n\n\n\n

            Contoh Soal 2<\/h3>\n\n\n\n

            Tentukan nilai trigonometri berikut ini.<\/p>\n\n\n\n

              \n
            1. tan(315o<\/sup>)<\/li>\n\n\n\n
            2. sin(210o<\/sup>)<\/li>\n\n\n\n
            3. cos(225o<\/sup>)<\/li>\n<\/ol>\n\n\n\n

              Pembahasan :<\/p>\n\n\n\n

              Mula-mula, tentukan dahulu letak kuadran sudutnya. Lalu, gunakan persamaan trigonometri di setiap kuadrannya!<\/p>\n\n\n\n

                \n\t
              1. \n\ttan(315o<\/sup>) \u2192 sudut 315o<\/sup> berada di kuadran IV<\/br>\n\tPersamaan yang berlaku adalah tan (360o<\/sup> – \u03b1) = -tan \u03b1. Dengan demikian:<\/br>\n\ttan(315o<\/sup>) = tan(360o<\/sup> \u2013 45o<\/sup>)<\/br>\n\ttan(360o<\/sup> \u2013 45o<\/sup>)= – tan(45o<\/sup>) = -1<\/br>\n\tJadi, tan(315o<\/sup>) = -1.\n\t<\/li>\n\t
              2. \n\tsin(210o<\/sup>) \u2192 sudut 210o<\/sup> berada di kuadran III<\/br>\n\tPersamaan yang berlaku adalah sin(180o<\/sup> + \u03b1) = -sin\u03b1. Dengan demikian:<\/br>\n\tsin(210o<\/sup>) = sin(180o<\/sup> + 30o<\/sup>)<\/br>\n\t\u2194 sin(180o<\/sup> + 30o<\/sup>) = -sin(30o<\/sup>) = -1\/2<\/br>\n\tJadi, sin(210o<\/sup>) = -1\/2\n\t<\/li>\n\t
              3. \n\tcos(225o<\/sup>) \u2192 sudut 225o<\/sup> berada di kuadran III<\/br>\n\tPersamaan yang berlaku adalah cos(180o<\/sup> + \u03b1) = -cos\u03b1. Dengan demikian:<\/br>\n\tcos(225o<\/sup>) = cos(180o<\/sup> + 45o<\/sup>)<\/br>\n\t\u2194 cos(180o<\/sup> + 45o<\/sup>) = -cos(45o<\/sup>) = -1\/2√2<\/br>\n\tJadi, cos(225o<\/sup>) = -1\/2√2.\n\t<\/li>\n<\/ol>\n\n\n\n

                Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"

                Hai Quipperian, di artikel sebelumnya Quipper Blog sudah pernah membahas konsep dasar trigonometri. Saat belajar trigonometri, pasti kamu akan bertemu dengan sudut istimewa, kan?…<\/p>\n","protected":false},"author":156742495,"featured_media":312826,"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":[679384865],"tags":[],"ppma_author":[679386821,679386836],"class_list":["post-312789","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"\nTabel Trigonometri Berdasarkan Kuadran dan Sudut Istimewa - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Tabel trigonometri adalah tabel yang berisi nilai trigonometri sudut-sudut istimewa, cek berdasarkan kuadran dan Persamaan Nilai Trigonometri Antar Kuadran serta contoh soal\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/tabel-trigonometri\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tabel Trigonometri Berdasarkan Kuadran dan Sudut Istimewa - 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