Aturan Sinus dan Cosinus - Materi Matematika SMA Kelas XI
![multimedia pembelajaran interaktif matematika bab aturan sinus dan cosinus multimedia pembelajaran interaktif matematika bab aturan sinus dan cosinus](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgB_JHGP86lLomWmdzBhRAASzgnFmwqrisUbtnGgsrIEEka-9t6y6zkFKH7ZM3pqQIiTH9z8kWxOj81xvB6835yazLPua5fjv5zwN-BaLgqFvAQ_JIbYexSdbYeVtqyK3U-X03GlTenPA/s1600-rw/Rumus-sinus.png)
Untuk anda yang ingin belajar langsung di sini, silakan anda pelajari materi dan beberapa contoh soal di bawah ini.
a. Rumus Penjumlahan Cosinus
Berdasarkan rumus perkalian cosinus, diperoleh hubungan penjumlahan dalam cosinus yaitu sebagai berikut.
2 cos A cos B = cos (A + B) + cos (A – B)
Misalkan
![](data:image/png;base64,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)
Selanjutnya, kedua persamaan itu disubstitusikan.
2 cos A cos B = cos (A + B) + cos (A – B)
2 cos 1/2 (α + β) cos 1/2 (α – β) = cos α + cos β
atau
![](data:image/png;base64,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)
Contoh soal dan penyelesaian penjumlahan Trigonometri.
Soal:
Sederhanakan: cos 100° + cos 20°.
Penyelesaian:
cos 100° + cos 20° = 2 cos 1/2(100 + 20)° cos 1/2(100 – 20)°
= 2 cos 60° cos 40°
= 2 ⋅ 1/2 cos 40°
= cos 40°
b. Rumus Pengurangan Cosinus
Dari rumus 2 sin A sin B = cos (A – B) – cos (A + B),
misalkan
A + B = α dan A – B = β, terdapat rumus:
![](data:image/png;base64,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)
Contoh soal dan penyelesaian pengurangan Trigonometri.
Soal:
Sederhanakan cos 35° – cos 25°.
Penyelesaian:
cos 35° – cos 25° = –2 sin 1/2 (35 + 25)° sin 1/2 (35 – 25)°
= –2 sin 30° sin 5°
= –2 ⋅ 1/2 sin 5°
= – sin 5°
c. Rumus Penjumlahan dan Pengurangan Sinus
Dari rumus 2 sin A cos B = sin (A + B) + sin (A – B),
misalkan
A + B = α dan A – B = β, maka didapat rumus:
![](data:image/png;base64,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)
Contoh soal dan penyelesaian penjumlahan dan pengurangan Sinus.
Soal:
Sederhanakan sin 315° – sin 15°.
Penyelesaian:
sin 315° – sin 15° = 2⋅ cos 1/2 (315 + 15)° ⋅ sin 1/2 (315 – 15)°
= 2⋅ cos 165° ⋅ sin 150°
= 2⋅ cos 165 ⋅ 1/2
= cos 165°
d. Rumus Penjumlahan dan Pengurangan Tangen
![](data:image/png;base64,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)
Contoh soal dan penyelesaian penjumlahan dan pengurangan Tangen.
Soal:
Tentukan nilai tan 165° + tan 75°
Penyelesaian:
![](data:image/png;base64,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)
Demikianlah sedikit uraian materi tentang rumus-rumus sinus, aturan cosinus dan tangen. Anda bisa mempelajari sifat-sifat dan operasi trigonometri lainnya trigonometri kelas 11Aturan Sinus dan Cosinus
Rumus Jumlah dan Selisih pada Sinus dan Kosinusa. Rumus Penjumlahan Cosinus
Berdasarkan rumus perkalian cosinus, diperoleh hubungan penjumlahan dalam cosinus yaitu sebagai berikut.
2 cos A cos B = cos (A + B) + cos (A – B)
Misalkan
Selanjutnya, kedua persamaan itu disubstitusikan.
2 cos A cos B = cos (A + B) + cos (A – B)
2 cos 1/2 (α + β) cos 1/2 (α – β) = cos α + cos β
atau
Contoh soal dan penyelesaian penjumlahan Trigonometri.
Soal:
Sederhanakan: cos 100° + cos 20°.
Penyelesaian:
cos 100° + cos 20° = 2 cos 1/2(100 + 20)° cos 1/2(100 – 20)°
= 2 cos 60° cos 40°
= 2 ⋅ 1/2 cos 40°
= cos 40°
b. Rumus Pengurangan Cosinus
Dari rumus 2 sin A sin B = cos (A – B) – cos (A + B),
misalkan
A + B = α dan A – B = β, terdapat rumus:
Contoh soal dan penyelesaian pengurangan Trigonometri.
Soal:
Sederhanakan cos 35° – cos 25°.
Penyelesaian:
cos 35° – cos 25° = –2 sin 1/2 (35 + 25)° sin 1/2 (35 – 25)°
= –2 sin 30° sin 5°
= –2 ⋅ 1/2 sin 5°
= – sin 5°
c. Rumus Penjumlahan dan Pengurangan Sinus
Dari rumus 2 sin A cos B = sin (A + B) + sin (A – B),
misalkan
A + B = α dan A – B = β, maka didapat rumus:
Contoh soal dan penyelesaian penjumlahan dan pengurangan Sinus.
Sederhanakan sin 315° – sin 15°.
Penyelesaian:
sin 315° – sin 15° = 2⋅ cos 1/2 (315 + 15)° ⋅ sin 1/2 (315 – 15)°
= 2⋅ cos 165° ⋅ sin 150°
= 2⋅ cos 165 ⋅ 1/2
= cos 165°
d. Rumus Penjumlahan dan Pengurangan Tangen
Contoh soal dan penyelesaian penjumlahan dan pengurangan Tangen.
Soal:
Tentukan nilai tan 165° + tan 75°
Penyelesaian:
Atau jika anda menginginkan rumus-rumus ringkasnya dan ingin mendownload rumus-rumus trigonometri di atas, anda bisa menuju rumus trigonometri
Untuk peta materi secara keseluruhan silahkan ke halaman ini
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