Rumus-Rumus Trigonometri
kumpulan rumus-rumus trigonometri matematika sma lengkap kelas 11
Rumus-rumus trigonometri yang dibahas disini fokus pada rumus-rumus trigonometri kelas XI ialah rumus-rumus trigonometri Jumlah dan selisih dua sudut, sudut rangkap , setengah sudut, perkalian sinus dan cosinus, jumlah dan selisih pada sinus dan cosinus dan identitas trigonometri.
Rumus-rumus trigonometri jumlah dan selisih dua sudut
Contoh soal:
1.Hitunglah dengan memakai teorema penjumlahan
a. sin 75°
[Penyelesaian]
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sDBWMKXb7zLMJQtbCuuoO6DHoJZKa7eMzLs5oSbbWpfj9XOhxS_t1GEkk_rWfr_L79BZ0PSH5eyAYKgDWAdxzfBDwoUKgexnNk4zBrPBKvzer7Veb24w6fqt2XLUhKsyYAQ0aDuKv4DcuipQ8URxehtdd3O_-MkEIP-4geNoVtNdK1jMNHzcwwQxQb1WjNkAnE8S371LJPdLXWfs7JzwrqdAmJ0HEaUhnIWrxPyN4ADz78IyMWB0kZEMN2m6QaDsR5zYvqe9DP2v3Pjm0L4sAxpagwfBDXcy_YNibEHxJ2Q4wh0LnV4TPT3xHIyqRxGNR3MmuYX8C1BJNVFk7eZrdghOHFukt-7RLrx68vFE11LZfLsuwE8lVDWvAxY5iVdFzNS8VpMQsFhBz_-ot0QKSuxKMdFXI157aubUAV8bB8CE6znGlI0Y3jiOwnesa6Aifq4fBl84kDPkTai31EQgvDuapo6Kdw0bjpWOAc6ctjiKOSehYieFTl_f96Z4bIWBdJ8t19Vdf3AkmZLx9X9vGbB1avxuD--Wp4FXOa3d39mxVt6jEVOhbqjZ_5uGkjepyo8-lOlUEtsg4JyXOSUxcTVJ-eluRf6XgQEoobjJ1JI-fh-JwZpchFU2BwQGjYea1b5TdRc-e-H_YTAHSlTDXn6C4YE3IUOAIcKZiZ0TCEffkIq1S5zTD5FaWxeg=s0-d)
![Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t4cwHMeRPS7KZkAL1cMSOc0g_niI86_4jdZDexVbmJA5QDezhd_VjLA6SiwyfvOvVELXw-TTh8i_ajv-4LMCQKE-k8IvN6QQVlv7WOrsk0583fNnMm5jNRMCqFGnSABZbROCSUnJLmQgmjdEb31u4f8L81VdQGuPiiyO-JebMZLr_aZRP0Mphsnn1AzEfASUT1YVN6XdAGZKV4mUFaP2xS32IzMh9DSlh0-Y5Ka-9txmxckBLRe1zEW3vFdv_Dm0tO7ZY0eN1UJ3PjyjLmn2TLsLAtr6m3-DsOSKYq5pKl2EGuxVLR-kv9vXnJyc1m451OEi4QZ5nLDbIcuVL_4LQqf8XtkHbJSjYUsK7KfaZf1lTUQqe8_vKty497PYYwRFgeQJEuyMkyewk_smmn=s0-d)
b. cos 105°
[Penyelesaian]
c. tan 15°
[Penyelesaian]
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s0MfweKdPF8BpUQosESQtqIyJy-TTftwE67izk468cAn3_7mMLgq3z0AVm-niPhHP7pqmbzdmQcCxFqKNI5g68IuX0wHE1tblEuN-LlalqdiC8RzNqpHWMQk4Y9lvCjlAMHg-ae5SPCWsKey8RQQc_LMiZpkFko77TOgLqz5QCgDabzfoRuySLQ0HCXgy5EfeyT37k8Cugc0ptziSs1T1W56nk9fig4IcxTxTWmG9bch3GEsB-O1r7vZ3OCm3R7tKHNKudGMK9xnt65l9rZPRESqNc5vtxIgpVTao6-N9WKYQ8zgkZ5RPvUUzJutc91-waRNb9JWprKUWfDFmaK-kxX23MNIAAwRcmS7Spg47lWHajujxUr24TA4vBQRNiN-KnqTAf_LChuyISKL_gwwvor_uJyHy-EI33lvfRIKbik437TcINvhpWKBxuyFOBIFENNnQOO3j1uhdpjYma8pe1n-672toxMUo0fsu2D3Bl7C4XfGU3GHDmB8hWDyOU_kAH6IjUokAnsx6V0F5w8h_2Ii9sdARive08D8v56lM62x70Gz0-C3Q1FSe6bo4qQwsHgiKCPnQQdZCD0iScIVE4N-KsAbpwiqSjNksshhs=s0-d)
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v_lVJ22SMIEonWZ3svXQY4AzXnXmqqHnk2CEWRItBg2h6dJ2nvIw9jeqLQ0TwtwlV38JNt350rPtrZ_uQzQTcgfhEWOXFlLJMSrtgqnCo63EtoT7vLMp1YqrOtQXr2wio4xhy3fUPXM5dVRWRQZwyAMdHY9evcuvJP7y-Zzg5fACIfhoi_cnOxOVB9n5Q3ib5pJhi60oqSu1iLPqsUw9em2OxN3YH3mygGNV2GbQMRg0WUJCpZ5W4=s0-d)
Rumus-rumus Trigonometri Sudut ganda atau rangkap 2α
Contoh Soal:
Tentukan nilai
jika ![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tSYVYmhfAlCP3xu-8yuoVHaimCdTGTaPzR2lJHefDlVcus3lONzAs400qs3Xh3H38ngufwFMdZDxuBNVyST1YQk-BtJGj6CGSWVnhGVCpa6cOb63dgZ6syiTUCfEo4b5I2CHmbJulnGWvJmpEPvysscpRbAaIOrD5TlQKmwsNZG_0iehXF7Uw5dXrI0MUWff-P6y3db7SmLgKlBCnFmFmlUtWAFpza6Q7-mAjsLMzaAPnzjkXz3s-J45ZMQfizQAqGTB5RTiCZjlnUDqdy4t8taWncHxPhC6ycSzFfgaxbBAA5MkHt5jrKQ1Gc656wfpgeWxarIfZ1TLtHTYIYQKxFQqqoFm7IFXJMyaln1keh27S-v9VXnhltQQJdH9j50LLY=s0-d)
[Penyelesaian]
Karena
, maka
dan
Jadi,
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t0hYWhhGwPctjM-iLygy4IRSyTQnVo0lcoAux8slM9rEG6A22U8oIoeGWXxfM6EiuZNJqR2kcNSgmZ9uL5oIDNgb7nF-E1rJd0T3svHPoNeHo4b2Fynew3Qogyaz95grHBfygXXSKTpeZitULB_k0tgD7Zn8hwVSziGuWirT6Mhk-bGyesIvaJ9uI-HDpR9BiAjtBGR_B1YmKnr3h5Dc_eW-EI7oj4hL_FK9RVDUSnXGqotQIeYAmNxBXHO5keB5nPEi0I5drcl8I2edYrAbxTtYii3ZsBj99T_Ch71szHa_I_qaAWMsYHj9WtwBO90vHdhZNu0VfUTwAqiUQxbz7L0TMf017TmYTZtpv9naGsF9hIYsMHYxr4r4fSpEzDv2LbVsvAr3onE8QAUMVnIvR_HWc--0kmcnTptzUH0SERcAYgTUoINp7cR0nChbwct-8zVECICLivPmPZf8Jx3NDj-_4GKz6woW4up-fffpswi_pTlH9X9nNLKT_LbBfK63DUrjgBBJLtM-4-2RFCmbP9U9ivH3sbrQFyPi4u=s0-d)
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u3igLfA____kkdYoKgEJV4M6OnpzYoKEosxeG7b18pH3U_dN8Fl0lnqMlgUmXcNzOETS5umEHXmZ-AnRlPRFBYK--0cHkFXM2d2_Hf5I0XQ0oh4c8hI2B0el6Da9HKieJGw5O1AEiVdWRgKF3edQx1En8TbF7KM3cKm8D8T2Ei_uW5rh3FcHItvhvMo1-vguee7fBhDDTii-HEogfkxnhs2drvD6uNlUUjGIX9lnMHhQF872M26t8M5BzTEpeMejzDgQE3s2kkZi8Kt102YXntm7XuCdRNhRrG7DshTNNEctM6RcikF0A2YdnaMLmsFri8sFF0eIZtswc4MncLkqjC732kHgEIHmV_r5DZaLvpVE6HsCa8vrW3hDM8m0nbPVkvF1jLZ0rwCO2LWzR6BVOPmEbt3aL8altrFouvA_upieXqAEXZwIMrTpcg8FMCJ5E12tD1bq4FNpKbuF0lN2wx2fAC1D5MiwYmfJbLr__67D5NWn6WLVHIJifaZ0sjttXpci4Yr6QXFIq6yce5UMSfP4CNKEetoxBbeN24A2KzlOik7TaoelaU7VMp2peqr9-F1NV6nghGSQAFujHJjL_KGpMufPZawUYsZUXoNXD3E9N53K1mWAGUHc7fnD2SLF2K=s0-d)
![Rumus-rumus Trigonometri rumus trigonometri Jumlah dan selisih dua sudut Rumus-rumus Trigonometri](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sa4dPIODUB8tNExi0gOIglTT2xFctxGcJ1VmkUidy5WV5MdMd0p-iTfEvTORSgRLSnLCh95mrXrXDTRsyMFzKyqbYsrqlffHNUbaKQwt-m9tm9QawMQJ10v6KLJ5s7z6F5z87PvwX1u_fKGyf97uLPgaJoFzObVdh-DAqhrJs5QgKYlLnDlW3yXYiccYCphaebM0yd094wl_7pTH7pbvqxxsWKUZEc4oOz8uGm1zPfV85C1CYbhPsYrfJgBhWd8YxSsHQ90qgjC4JbPJCyVcqrxqvy27pX9sg3nHWzXHbt37WD-CM5RJEs7bhqWRAAEL183FDLOZ_LtRXt4DulJRa6J-uopjOsxEzJH_4350HhDoIsnjK_AYQ4dHyxyL3RvSjNztG9XgzC6DP3YU7FeGnVyXDNnmwfcZZL6Ofienk3sA33b7LB-LJCAaujDVsCCKayTvvSLC8MO-OQtqpVfTA=s0-d)
Karena
Jadi,
Rumus-rumus Trigonometri Sudut ganda atau rangkap 3α
Rumus-rumus Trigonometri Setengah Sudut sinus , cosinus dan tangen sudut ½ α
Rumus-rumus Identitas Trigonometri
Semoga bermanfaat! rumus-rumus trigonometri ini sangat berkhasiat dan bahan prasyarat untuk turunan fungsitrigonometri, limit fungsi trigonometri, dan juga integral fungsi trigonometri dan bahan kalkulus ibarat turunan fungsi implisit. Dengan rajin berlatih mengerjakan soal menghapal rumus-rumus trigonometri akan lebih cepat dan lebih usang diingat, Jika ada yang salah dalam artikel ini silahkan tinggalkan kritik dan saran dikolom komentar dan like juga ya.. fanspage facebook nya, selamat berguru rumus-rumus trigonometri.
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