Jembatan Keledai Untuk Nentuin Nilai Trigonometri

29 Agustus 09

nilai_trigonometri
Suatu ketika kita dibingungkan untuk menentukan nilai sinus, cosinus dan tangen dari sudut istimewa yang bukan di kwadran I. Dalam pelajaran trigonometri ada 17 macam sudut istimewa yaitu:
0^0, 30^0, 45^0, 60^0, 90^0, 120^0, 135^0, 150^0, 180^0, 210^0,225^0, 240^0, 270^0, 300^0, 315^0, 330^0, 360^0 Tentu saja kita akan kesulitan untuk menentukan nilai trigonometri dari semua sudut tersebut. Tapi ada satu cara yang membuatnya menjadi lebih sederhana, eits.. tapi syaratnya kalian harus tahu terlebih dahulu nilai trigonometri dari sudut istimewa dari 0 sampai 90. http://www.kaskus.us/images/smilies/tabrakan.gif
Nah sekarang kita akan membuatnya menjadi sederhana dengan klu-klu yang saya berikan yaitu:

  1. Sudut istimewa di kwadran II, III dan IV dapat dimanipulasi dari penambahan atau pengurangan dengan sudut 180 dan 270, sepakat?
  2. OK, berarti intinya kita manipulasi dalam penjumlahan dan pengurang dengan 180 dan 270 dicari yang paling dekat.
  3. Pikirkan nilai trigonometri dari sudut tersebut apakah negatif atau positif dengan aturan seperti pada gambar.
  4. Yang terakhir, jika dihubungkan dengan 180 sin tetap sin, coc tetap cos, sedangkan jika dihubungkan dengan 270 sin jadi coc, dan cos jadi sin.

Sekarang kita lanjutkan ke contoh..

  1. Misalkan kita akan mencari nilai sinus 120.
    1. Maka yang kita pikirkan pertama adalah nilainya positif or negatif, karena di KW II maka sinusnya positif.
    2. Lalu, sin 120^0=sin (180-60)^0=sin 60^0 = 1/2sqrt{3} Karena yang dihubungkan dengan sudut 180, maka sinus tetap sinus.
  2. Trus contoh lagi, carilah nilai cos 240!
    1. Maka yang kita pikirkan pertama adalah nilainya positif or negatif, karena di KW III maka cosinusnya negatif.
    2. Lalu kita bisa menghubungkan dengan 180 atau 270 terserah, tapi disini tak kasih contoh pake dua-duanya.
      1. Kita pake 180 ya,…cos 240^0=cos(180+60)^0=-cos 60^0=-1/2 Tanda jadi minus karena 240 di KW III jadi cosinusnya negatif
      2. Ne kalo pake 270,.. cos 240^0=cos(270-30)^0=-sin 30^0=-1/2 Disini cos jadi sin karena dihubungkan dengan 270. Hasilnya sama bukan?

Nah gitu caranya. Oh ya untuk nilai tangen bisa didekati dengan rumus tan a = {sin a}/ {cos a} :)
Sekarang giliran kalian untuk mencari nilai-nilai yang lain.. sante aja ndak da yang ngejar kok kecuali waktu ujian yang udah hampir habis. 😉

18 responses to “Jembatan Keledai Untuk Nentuin Nilai Trigonometri”

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    Keren banget deh..akku nyari ini buat tugas kuliah fisika..hhe..
    permainan yg mnyenangkan..

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    macih bingung, kenapa hasilnya jadi gitu……………

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    kenapa disebut jembatan keledai??
    ada alat peraganya gak??

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    mantap…
    berguna banget nie bwt final ntar….

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