Pada materi kali ini akan membahas tentang jumlah dan selisih dua sudut dalam trigonometri yaitu pada sinus, cosinus, dan tangen.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHep6f1ByJiTzz52Bc5AdhdDFC6jKyn0D4xIOvBrtknoOdAINutEmMqVmY4cIcx4tMJPw6D6ibQJKYFtPZWJGV4rNEgwRF8ddZCUZnuTX1BZyVvioRRuGO4Q6rIeXJ0Q1BxIiG23OR5NU/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+2.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1WMUfehokQQDvLEoI5voLCdVdbXqFXsyWhhYWWp7MDn6sNiJdTE1WVcN3Jn2bgSSmbRgHmOkXf32elsKgaqhiRhcM6quvUFoFqjdRyXCdfO1U6VObjDiBsxhAOF-i6Hn_N6mm0HkEJXo/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+3.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMiHb_orp39s1Z3UPEnuLJPhGx5enlfCgDBQMb8LNxBHUrW-R796NQx4kkCgIpcelfGwLLiSNE5l1chfUZ2T_TvLlh0vNjabUqvJeei-WhGSuUBl2ATgK6nW8PyKNivcEB02AOhpCFkuM/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+4.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP1G6wt77W2Ac6ReN_-iHSpqG0Lf-T07VNxwiv_oGjzZrb1SOJkiNmdNDlmNcBgobD3rK9n7bfOPQ9WK4SS7WN6rxa8g-Ayx3uWdv5glaH4J2syB3KkTm6qq6gFanC0qO4pkgd3gxDfYg/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+5.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIlTTN0knCKRhGx6I3_nNbQEGxdBr3hIkOUGtfeIby70vIMpOa09_DfkXra0rnB1LiNUJqaoTbnmyrcNeytbn5Rlq_AAL2H1uOfhX-xmP30S9nfnI5B1ruxLKG6h4YU2Gje6RrdasDC7o/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+6.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPpWqX66fYsl5x1DMwYlM93d-WmPvBmdsJ4yrW_UvS9ioUIcb12ZpWuDe7grVd7Gvj33UZEd4__6QD4ZYT-M06ETWlZAQT-p0cFTwh6-zFuC5tVX3m9xNwGnNHjI0OOH__QeGco79aqas/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+7.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeaqgn0-e9tMGblbvUbL3GlOAssqE9ka3UUaJgBhh8crn4rulIU8CC56dtI2IGk5pxPVzevQ1Pv0AKL3KZ12bhA12NVkzliIAweesVarXkdsHmYyoeXZgZ0Kh1aqqiPDyiRd9egNDroGA/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+8.JPG)
02. Tentukanlah nilai dari:
(a) sin 15o
(b) sin 285o
jawab
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFIxJ8E1ufGJnppvZiynGBRT4gyf947gbJ06wNMYGGzanrU3WUml52CHKo4DzZS8Cl_IotP7DKMtdaaltqg2pR3mDNzgdQ4Me0UKWQCs8HDJ7OMUAwFusPBMSOdjd7EvHJkPZmYrr5VzY/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+9.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoc8YKUqJ4Ya33eRLZez1A21loZxTNzEu5FW7ZRkPuv1cRb7-zXTknt4i87LJFiZ7OnO9wXoCqseyHazzKYqLeOsDLxZG_rQQYK0SYuPMpg-EAXSbS-yoPh1YkKCFwRiOqdNWvL-JLwM4/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+10.JPG)
03. Tentukanlah nilai dari:
(a) tan 105o
(b) tan 255o
Jawab
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4baBmGK9y76vbbOrq2Yc9C8L1zYRI1ghCxtakSzMXsGrJojstodIdM7Jkk9_wSx4s8m3asoI4FvpvPfZf3mxzupGzRRBx-zfm9Hi_EkU_urnWZIeBbt0JykewDai0IpujaP875wSQsRQ/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+11.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5VLZ8JTp3l_hAZQRnPMBOqpwf2ccLDX6EdIBUiQxeecM2aSccMfT8alLwKqcRtPvdSJ4dAV2Ofsp3NfvpRmYDFydto_WtlUpb0Ciss_YLLIQgRmTCkLTVvdICAi6CDRn0ZnoC8zFXugw/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+12.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhh1EABzPe4A9ygnUSCuE9F1WBHJTXFKo6GrH_RB1-77nM-zZxHi79PhIh8YABinVIXH1GAwdyWNAzpGMvAiH4UmbQ98mjKn7p-_QfPkoOVgD5QyfJm2xn2e9e4x3fmwM48HbV_-7C4nYg/s200/Rumus+Jumlah+dan+Selisih+Dua+Sudut+13.JPG)
04. Tentukanlah nilai dari :
(a) sec 255o
(b) cot 345o
Jawab
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJvu5bomJcPgLoWYgliiG4yARsoN_W9w6t1vlxL4jYTspk-_-B2gtk910BEpJR0_4-NuQK_N8N20iSvoND72ifWcW5fEQ2zxC5t2TP6wD7UYHVZB-HpmuyWX3v7gaCDHnMTxWlLZz9v9c/s400/Rumus+Jumlah+dan+Selisih+Dua+Sudut+14.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOyctIWAdRAopPwVgO_k-GMjO82y_V16lYyhpO7cBKkK-NkRPXVQlsl2O7J8dORoLpQ2F_s80emR8ciAzkl_B9uvtk66b1Zst0ySs5ef9vHbgBlYeyw-ErhullauwpYMPWJ-QtRGvCvpU/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+15.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl3SYxU0HaKYR-QMSu_wcUAivkllz_bu8WZI0xdSuAQN4QJyHZ4unOeijVqM1mEvkwyVZYH6ls1mDiJrm3KKzCi13Ft-hzYuXlkgUwHHB7HPTD7Lo-CWBKk6-AQUx4OmfrAl8-QMOsZos/s200/Rumus+Jumlah+dan+Selisih+Dua+Sudut+16.JPG)
05. Diketahui sin α = –4/5 dan cos β = 7/25, dimana α sudut di kwadran III dan β di kuadran IV. Tentukanlah nilai dari:
(a) sin (α + β )
(b) cos ( α – β )
(c) tan( α + β )
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhitZECKZooCWaVTHC5SE-N8pq4pXkjP4AxpWP_CCvKg2DN0oQqVIJ3EJOLAp0f03Hzmiu6qoLHAdGoIa6kzuuUs8_NbyQC2LwQTfooa7iD5CTu5GirMlH_rLLKaF-vUHSlFle5Me1FTTc/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+17.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWx3s7Sz_agcSBMfFPBdSvQCpBDQ52tvfUfsqvLFPerFDSSIKfAYg8pghG86EhrKhlZs0t5j1-oL0L3-SAkPCNffAMfIsEru1qvKWfLFuCQBhlPhJhagecXd4u0EMEb8jc20tg1GDuha8/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+18.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjERctq63jpg4QL2EV3iNlNsMGndzx5nr0rewGWalOzHLeE_3ijMvuVFrm6B2jBrYnaYybo7nkuq4Cgryj7JXywQ3taLETSq1758rg31_jNjBG_eEfhyphenhyphen1jMUm5v_vET8hu3lXDKjNdS6qk/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+19.JPG)
06. Buktikanlah bahwa cos(A + B).cos(A – B) = cos2A – sin2B
Jawab
Ruas kiri = cos(A + B).cos(A – B)
= (cosA.cosB – sinA.sinB)( cosA.cosB + sinA.sinB)
= cos2A.cos2B – sin2A.sin2B
= cos2A.(1 – sin2B) – (1 – con2A).sin2B
= cos2A – cos2A.sin2B – sin2B + cos2A.sin2B
= cos2A – sin2B
= ruas kanan
Rumusnya adalah sebagai berikut:
01. Tentukanlah nilai dari:
(a) cos 75o
(b) cos 165o
Jawab
02. Tentukanlah nilai dari:
(a) sin 15o
(b) sin 285o
jawab
03. Tentukanlah nilai dari:
(a) tan 105o
(b) tan 255o
Jawab
04. Tentukanlah nilai dari :
(a) sec 255o
(b) cot 345o
Jawab
05. Diketahui sin α = –4/5 dan cos β = 7/25, dimana α sudut di kwadran III dan β di kuadran IV. Tentukanlah nilai dari:
(a) sin (α + β )
(b) cos ( α – β )
(c) tan( α + β )
06. Buktikanlah bahwa cos(A + B).cos(A – B) = cos2A – sin2B
Jawab
Ruas kiri = cos(A + B).cos(A – B)
= (cosA.cosB – sinA.sinB)( cosA.cosB + sinA.sinB)
= cos2A.cos2B – sin2A.sin2B
= cos2A.(1 – sin2B) – (1 – con2A).sin2B
= cos2A – cos2A.sin2B – sin2B + cos2A.sin2B
= cos2A – sin2B
= ruas kanan
Sangat Bagus bukk
BalasHapusNomor 5 yg a, sama nilai tan-nya ada yang keliru. Mohon diperbaiki
BalasHapusHuahahahahaa
BalasHapus