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/AVvXsEjJAu2U499x4BOwtmjuWoSJR7hoNDuJynGk090w1bD7_WkgtQEysJIe3z9yUYtOwvwAQDKCcEFBs5kNtPdDtpn0hm61RxF_Jbx5fwkvmWVdQSum-Le-wzJlPOcCNBDxtobLTkhHh80_El0/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+2.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQArD3YK0DKE-3BrZpzmTQBm7pSTic7nm8OAK8bJqtwVU5vxWRzcZZtanwhPb0SAYMv_zoZjlrNwjpDY7g9JEhSD681Zzf2kvhTKpj_e0V2pmZ6cMjBNwKdlwPA8UDlHvNwhTmk4E5TdQ/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+3.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsMnHVre-oW5uxN9UDKCqjetRy47cthaJoBdR4ru1-dJ7YlKI78p8j9_rvtzIrjUEdmcCha9bQ0mtLmFH-3IFa41oRU6mgF7VxbGIu5oedeiyVBd92g7qb2J5OtYUQLC2Ad_H9e97WdBg/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+4.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5o6Z9polV8z52QuSLY9Ga6PCHAsHQ0HczoDIXLyQu8sCx71scUcqw00nIDseLAS3p0n77bZpLs3RlsmsKSzQkAfLDVWDz1ipdnuQ4b-yVnjrPwwgRWwym3jFF3msPNSwoIX-OiTLBpOc/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+5.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUHsR8_kgCYD38Sy4kka0xrY7zXGjZpaxVhIWlF4h7NAejMMBfwu9ve1rzvPxVbMHPhNi4X01CZEbB0iUcuzBCNFiow8rB_G_7P5cwfX3NkCqauLIGUg1OEnMEr_l9Dj_Wk6CCxgWItsM/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+6.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXPq4S-UJfdtxbgop0LVTqb4eR79P1P85x9RSZwykbOODGAsUvfl4NqVkOlXN0FO2jeSwqyC2ZWm0TvNJUmgKJKBQq_P-FJdGUd2N61Zvdnz6vo016EjPXzZhBujG49ugLrQMOT6hFY1Q/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+7.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzlSUJvdjJXd_xvRyggwzuUbIbPntVUPT-ehTH8hTpkKX5xwEfbfeCOIshibNfOvEA2KRP8rMHx3FIn6sfnJYpfeRC9VTT_SjwrlzyYFGzNCaVlOOI6-UEf0AD5ux-1l_pDjyPbNBizHA/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+8.JPG)
02. Tentukanlah nilai dari:
(a) sin 15o
jawab
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheg7NBs40oSQJEH2SucAar6A5W3jd5LXudy2pFkKu4LiP67OSFDoWfuxQ45anm7UsGwo9Ww6zN-dAB24yCrMffuN_8weXOatQ-wYks8r_3HhCGJZbeuvybeDxVQ4hGh6iGFTAx04ZO2KQ/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+9.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIZChOzcr1iCYUCuC3L7RXROXxN6zuepZoWxmcT138BiI-RcLk2uK3iNSzYNQszG4IwfG1NEJVA9SJCzQ6mVEfZNI0cUHu3K5Rcnmq97ymgY4S-wrrMYNChI5czvGzju9fInAn2hIpF-c/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/AVvXsEglLt3z-zMmYAVxpmAY9tLLS3j1EVJNPsLG3okJYotJqG72YSm92QlERU5cN7xZSYP4NWkl2vgMF2t9Sd2apoAtJ8wYVnXWxg-kl9p5hHk1msJARPrfft4YK8HJ5asoBoskPz5vyUzsjxQ/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+11.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMsDLAI2zo1mrgJSJebK2a96DkP6wPTH-ei1KRislpzTAVvFuOGPBk7UJWfNS0EVrzt10UX1QoYEgz28RIDfrcWay9uIk3YRKQJs_2TYcClNPTFasqw7vArGwFZRcN5YC_BdHAlnYBcpY/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+12.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHlwye4lRalXFaFIHccfGSft_RamptWcW12n6gycEIXUgBIGdXAcAS8xeKeh5mebyB914Lw5eDoOj_8ZltVjfgn3KRggQYP3TSE64avsl5Lfy2r25epcmYlQXyXKT_Ni0hcITkRxqxiuM/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/AVvXsEjBDZEYb4_3xxc66l7evnyuSEVzvmxWj-sbPj1aIfgW0vrWjyrke0Ad0vWA-L3goJLDZJbHmgsuoKnYXDBQ7nVNAC3P4MXBBzIP7GmYnZ4sVH0NF6E1zmHhdZQiHSdEBmqhZ4ckO1IVCXc/s400/Rumus+Jumlah+dan+Selisih+Dua+Sudut+14.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5OWLN_yeQNw0e8sxKSzCV0eZw8JaMhNfs_8vBgN1l50GL5zC00j924osmJRsKAO8UD4hqzphWxwH3jkYM4SLAwgS5vjqqgVUyi_ihWejJ2jfRXfLvfGTmeTF8hU-F31S5aPcz8giawO8/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+15.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbJ3el_D7g6t19iP8kkoVL5ZgrN58gSwyiO8mEfdXynS_yYQ1wNEhj_4QO3MiCMxaFTRJfT7oIXtyELckuWfN964dlUJGwSxGV20Bp-Ek-2ad26DBEWQ9yt2fgl1UMNPxHBC4kK_AFpUo/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/AVvXsEjHUFMUAcJbaaJuP3bGBiEtDL-1lQvN9uqpypD1CQuD1vp9q3UCMJnVwVU9fXRTKhoGwXuGuXVYftmEKkfqS_W6KGmlH58Wb8JBv6u5cW8eLu2WXijlryusgK9-BT9f7p5WIiGoqfcW4iQ/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+17.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU68laDEPV-VYIuFnAHlLvEZpdyJc6jL22U6C3S4kL_TnNeDHqxlQZfrgHx3skYTOKW2-p2izQbWLG5HrUWE8bXNw_-IXL256KJ69qMNuLekNuyOH-CK_Ld7EA4yu1245AVHfS1txGiR4/s320/Rumus+Jumlah+dan+Selisih+Dua+Sudut+18.JPG)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsNCTRvYyVQdDou-6se9BzZlxY8NCeJBpR1lyVVmnt7lDgUipgTOQB76Bzcwx01dquQHpV-uRPeKV9VDHAgADliVnNgPWX0jDcvaOqJZDDWxI5v3JItCJqRrBaBsyHsnisBdUtynqvlw8/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
01. Tentukanlah nilai dari:
(a) cos 75o
(b) cos 165o
Jawab
02. Tentukanlah nilai dari:
(a) sin 15o
(b) sin 285o
03. Tentukanlah nilai dari:
(a) tan 105o
(b) tan 255o
Jawab
04. Tentukanlah nilai dari :
(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
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