SKRIPSI Jurusan Matematika - Fakultas MIPA UM, 2010

Ukuran Huruf:  Kecil  Sedang  Besar

Fungsi Trigonometri Dengan Pendekatan Barisan Fungsi

RIZAL WINARKO

Abstrak


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ABSTRAK

 

Winarko, Rizal, 2010. Fungsi Trigonometri Dengan Pendekatan Barisan Fungsi. Skripsi. Jurusan Matematika FMIPA Universitas Negeri Malang. Pembimbing: ( I ) Dr. Sisworo, M.Si., (II) Drs. H. Imam Supeno, M,S.

 

Kata kunci : barisan fungsi, fungsi trigonometri.

 

Pada umumnya, pendefinisian fungsi trigonometri dilakukan pada segitiga referensi (reference triangle) untuk sudut  dalam posisi standar. Misalkan  adalah panjang sisi depan ,  adalah panjang sisi samping  dan  adalah jari-jari atau jarak dari titik asal ke . Diberikan   dan  dengan

Selain itu, fungsi trigonometri dapat dibahas dengan pendekatan yang berbeda, yaitu dengan barisan fungsi. Awalnya, diberikan suatu teorema tentang eksistensi fungsi trigonometri. Pada pembuktian, pertama, didefinisikan suatu barisan fungsi yang kontinu secara induktif. Barisan fungsi tersebut konvergen seragam ke suatu fungsi dan limit dari barisan fungsi tersebut didefinisikan sebagai fungsi trigonometri, yaitu  dan  untuk . Setelah itu, teorema eksistensi tersebut dibuktikan ketunggalannya. Berikut beberapa sifat fungsi trigonometri yang telah dibuktikan dangan terminologi barisan fungsi.

1.         dan