{"id":3118,"date":"2025-10-28T14:00:27","date_gmt":"2025-10-28T07:00:27","guid":{"rendered":"https:\/\/example.com\/?p=3118"},"modified":"2025-10-29T14:03:11","modified_gmt":"2025-10-29T07:03:11","slug":"memahami-fungsi-trigonometri-sederhana","status":"publish","type":"post","link":"https:\/\/www.ruangguru.com\/blog\/memahami-fungsi-trigonometri-sederhana","title":{"rendered":"Memahami Grafik Fungsi Trigonometri Sederhana dan Contohnya | Matematika Kelas 10"},"content":{"rendered":"<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"width: 820px; margin-left: auto; margin-right: auto; display: block;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Mengenal%20Fungsi%20Trigonometri.jpg\" alt=\"Mengenal Fungsi Trigonometri\" width=\"820\" \/><\/p>\n<blockquote>\n<p style=\"text-align: center;\"><em><span style=\"color: #000000;\">Belajar fungsi trigonometri sederhana, yuk! Ada fungsi sinus, fungsi cosinus, dan fungsi tangen. Simak pembahasan beserta gambar grafiknya di <strong><a href=\"https:\/\/www.ruangguru.com\/blog\/c\/matematika\/matematika-sma-kelas-10\">artikel Matematika kelas 10<\/a><\/strong> ini!<\/span><\/em><\/p>\n<p style=\"text-align: center;\"><em><span style=\"color: #000000;\">&#8212;<\/span><\/em><\/p>\n<\/blockquote>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Pada materi sebelumnya, kamu sudah mempelajari tentang <a href=\"\/blog\/apa-itu-trigonometri\" rel=\"noopener\"><strong>trigonometri secara umum<\/strong><\/a><span style=\"font-weight: normal;\">. Nah, kali ini, kamu akan mempelajari materi lanjutannya, yaitu <span style=\"font-weight: bold;\">fungsi trigonometri<\/span>. Apa yang dimaksud dengan fungsi trigonometri?<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-weight: normal;\">Fungsi trigonometri adalah <strong>suatu fungsi yang grafiknya berulang secara terus menerus dalam periode tertentu<\/strong>. Seperti terlihat pada header di artikel ini, grafik fungsi trigonometri terdiri atas <span style=\"font-weight: bold;\">bukit<\/span> dan <span style=\"font-weight: bold;\">lembah<\/span> yang berulang-ulang secara terus menerus dalam periode tertentu. Oh iya, gambar grafik yang ada di header itu adalah gambar <span style=\"font-weight: bold;\">grafik fungsi sinus<\/span>, ya! Nanti akan kita bahas lebih lanjut di artikel kok, tenang aja, <em>hehe<\/em>&#8230;<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Unsur-Unsur Grafik Fungsi Trigonometri<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-weight: normal;\">Pada fungsi trigonometri terdapat beberapa unsur, yakni <span style=\"font-weight: bold;\">periode, amplitudo, nilai maksimum, <\/span>dan <span style=\"font-weight: bold;\">nilai minimum<\/span>. Kita bahas satu per satu, ya.<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">a. Periode<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Periode adalah j<span style=\"font-weight: bold;\">arak antara dua puncak atau dua lembah pada grafik fungsi trigonometri<\/span>. Atau dapat diartikan juga sebagai jarak terjadinya grafik fungsi trigonometri tersebut berulang.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">b. Amplitudo<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Amplitudo adalah <span style=\"font-weight: bold;\">setengah dari selisih nilai maksimum dan minimum dari suatu fungsi<\/span>. <span style=\"font-weight: bold;\">Rumus<\/span> amplitudo yakni sebagai berikut:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" style=\"width: 173px; display: block; margin-left: auto; margin-right: auto;\" title=\"amplitudo\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/amplitudo.png\" alt=\"amplitudo\" width=\"173\" data-constrained=\"true\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">c. Nilai Maksimum<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum adalah <span style=\"font-weight: bold;\">nilai tertinggi<\/span> yang bisa dicapai oleh suatu fungsi trigonometri. Pada grafik, nilai maksimum merupakan <span style=\"font-weight: bold;\">titik puncak<\/span> dari <span style=\"font-weight: bold;\">bukit<\/span>.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">d. Nilai Minimum<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum adalah <span style=\"font-weight: bold;\">nilai terendah <\/span>yang bisa dicapai oleh suatu fungsi trigonometri. Pada grafik, nilai minimum merupakan <span style=\"font-weight: bold;\">titik terendah <\/span>dari <span style=\"font-weight: bold;\">lembah<\/span>.<\/span><\/p>\n<p style=\"text-align: justify; font-weight: bold;\"><span style=\"color: #000000;\">Baca Juga: <a href=\"\/blog\/persamaan-trigonometri-sederhana\" rel=\"noopener\">Bentuk Persamaan Trigonometri Sederhana dan Contohnya<\/a><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Jenis-Jenis Grafik Fungsi Trigonometri<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Fungsi trigonometri sederhana terdiri dari tiga macam atau jenis, yaitu <span style=\"font-weight: bold;\">fungsi sinus<\/span><span style=\"font-weight: normal;\">,<\/span><span style=\"font-weight: bold;\"> fungsi cosinus<\/span><span style=\"font-weight: normal;\">,<\/span> <span style=\"font-weight: normal;\">dan <\/span><span style=\"font-weight: bold;\">fungsi tangen<\/span>. Nah, masing-masing fungsi tersebut dapat dijelaskan menggunakan <span style=\"font-weight: bold;\">grafik baku fungsi trigonometri<\/span>. Kita bahas satu per satu, ya!<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">a. Grafik Fungsi Sinus (y = sin x)<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai dari sinus adalah <span style=\"font-weight: bold;\">-1 \u2264 sin(x) \u2264 1<\/span>. Untuk gambar grafik fungsi sinus dapat kamu lihat pada infografik berikut.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/grafik%20fungsi%20sinus%20y%20=%20sin%20x.jpg\" alt=\"grafik fungsi sinus y = sin x\" width=\"600\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Pada grafik fungsi sinus berlaku:<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum = 1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum = -1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Amplitudo = 1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Periode = 360\u00b0<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">b. Grafik Fungsi Cosinus (y = cos x)<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai dari cosinus adalah <span style=\"font-weight: bold;\">-1 \u2264 cos(x) \u2264 1<\/span>. Untuk gambar grafik fungsi cosinus dapat kamu lihat pada infografik berikut.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/grafik%20fungsi%20cosinus%20y%20=%20cos%20x.jpg\" alt=\"grafik fungsi cosinus y = cos x\" width=\"600\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Pada grafik fungsi cosinus berlaku:<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum = 1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum = -1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Amplitudo = 1<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Periode = 360\u00b0<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; font-weight: bold;\"><span style=\"color: #000000;\">Baca Juga: <a href=\"\/blog\/fungsi-komposisi\" rel=\"noopener\">Belajar Fungsi Komposisi &amp; Contohnya, Lengkap!<\/a><\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 14pt;\">c. Grafik Fungsi Tangen (y = tan x)<\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Grafik tangen <span style=\"font-weight: bold;\">tidak mempunyai nilai maksimum<\/span>. Untuk gambar grafik fungsi tangen dapat kamu lihat pada infografik berikut.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/grafik%20fungsi%20tangen%20y%20=%20tan%20x.jpg\" alt=\"grafik fungsi tangen y = tan x\" width=\"600\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Pada grafik fungsi tangen berlaku:<\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum = Tidak ada<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum = Tidak ada<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Amplitudo = Tidak ada<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Periode = 180\u00b0<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Selain itu, terdapat pula <span style=\"font-weight: bold;\">grafik tidak baku<\/span> pada fungsi trigonometri yang <span style=\"font-weight: bold;\">lebih kompleks<\/span>. Grafik tidak baku ini<span style=\"font-weight: bold;\"> digambar berdasarkan fungsi<\/span> seperti tertera dalam tabel berikut.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/tabel%20fungsi%20trigonometri%20tidak%20baku.png\" alt=\"tabel fungsi trigonometri tidak baku\" width=\"600\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"background-color: transparent; text-align: justify;\">Untuk contoh gambar grafik fungsi trigonometri tidak baku akan dibahas pada materi selanjutnya, ya. <em>Stay tuned<\/em> terus di ruangbaca, okeyy!<\/span><\/span><\/p>\n<p style=\"text-align: justify; font-weight: bold;\"><span style=\"color: #000000;\"><span style=\"background-color: transparent; text-align: justify;\">Baca Juga: <a href=\"\/blog\/matematika-kelas-10-membuat-fungsi-kuadrat-dari-grafik\" rel=\"noopener\">Cara Menyusun Persamaan dari Grafik Fungsi Kuadrat<\/a><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"background-color: transparent; text-align: justify;\">Nah, sekarang kita coba kerjakan <\/span><span style=\"font-weight: normal;\">contoh soal<\/span><span style=\"background-color: transparent; text-align: justify;\"> di bawah ini aja, ya!<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"font-size: 18pt;\">Contoh Soal Fungsi Trigonometri<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">1. Tentukan nilai maksimum dan nilai minimum dari fungsi trigonometri di bawah in!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">a. f(x) = 2 sin 2x + 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">b. f(x) = -3 cos (3(x+90\u00b0)) &#8211; 8<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Penyelesaian:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">a. f(x) = 2 sin 2x + 5 \u2192 a = 2 , c = 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum = |a| + c = |2| + 5 = 7<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum = -|a| + c = -|2| + 5 = 3<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">b. f(x) = -3 cos (3(x + 90\u00b0)) &#8211; 8 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">f(x) = &#8211; 3 cos (3x + 270\u00b0) &#8211; 8 \u2192 a = -3 , c = -8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai maksimum = |a| + c = |-3| + (-8) = 3 &#8211; 8 = -5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Nilai minimum = -|a| + c = -|-3| + (-8) = -3 &#8211; 8 = -11<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\"><em style=\"background-color: transparent;\">&#8212;<\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Beg<span style=\"background-color: transparent;\">itulah materi kita kali ini tentang fungsi trigonometri sederhana, yang terdiri atas fungsi sinus, fungsi cosinus, dan fungsi tangen. Semoga kamu paham ya, dengan penjelasan di atas. <em>Eits<\/em>, kamu juga bisa mempelajari lagi materi ini melalui <\/span><a href=\"https:\/\/www.ruangguru.com\/ruangbelajar\" target=\"_blank\" rel=\"noopener\"><strong style=\"background-color: transparent;\">ruangbelajar<\/strong><\/a><span style=\"background-color: transparent;\">, lho! Yuk, <em>download<\/em> sekarang!<\/span><\/span><\/p>\n<p><a href=\"https:\/\/bayar.ruangguru.com\/\"><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/e3260f88-1749-4d3b-8973-be3aae07a94c.jpg\" alt=\"CTA Ruangguru\" \/><\/a><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Referensi:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sinaga, B.,\u00a0dkk. (2017). <em>Matematika<\/em>. Jakarta: Kemendikbud.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Belajar fungsi trigonometri sederhana, yuk! Ada fungsi sinus, fungsi cosinus, dan fungsi tangen. Simak pembahasan beserta gambar grafiknya di artikel Matematika kelas 10 ini! &#8212; &nbsp; Pada materi sebelumnya, kamu sudah mempelajari tentang trigonometri secara umum. Nah, kali ini, kamu akan mempelajari materi lanjutannya, yaitu fungsi trigonometri. Apa yang dimaksud dengan fungsi trigonometri? Fungsi trigonometri [&hellip;]<\/p>\n","protected":false},"author":10,"featured_media":3118,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Mengenal%20Fungsi%20Trigonometri.jpg"],"_edit_last":["1"],"_edit_lock":["1761721250:1"],"_wp_old_date":["2022-04-22"],"_yoast_wpseo_primary_category":["467"],"_yoast_wpseo_title":["Memahami Grafik Fungsi Trigonometri Sederhana dan Contohnya"],"_yoast_wpseo_metadesc":["Belajar fungsi trigonometri sederhana, yuk! Ada fungsi sinus, cosinus, dan tangen. Simak pembahasan beserta gambar grafiknya di artikel ini!"],"_yoast_wpseo_content_score":["90"],"_yoast_wpseo_estimated-reading-time-minutes":["5"]},"categories":[467,474],"tags":[52,10,37],"class_list":["post-3118","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","category-matematika-sma-kelas-10","tag-kelas-10","tag-konsep-pelajaran","tag-sma"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Memahami Grafik Fungsi Trigonometri Sederhana dan Contohnya<\/title>\n<meta name=\"description\" content=\"Belajar fungsi trigonometri sederhana, yuk! Ada fungsi sinus, cosinus, dan tangen. 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