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Diketahui  dan sudut  terletak di kuadran I. Tentu...

Diketahui sin space a equals 2 over 5 dan sudut a terletak di kuadran I. Tentukan nilai perbandingan trigonometri lainnya !

Jawaban:

Gunakan perbandingan sisi pada trigonometri menggunakan penamaan (de, sa, mi) untuk mendefinisikan nilai perbandingan trigonometri.

Diketahui:

  • sin space straight a equals de over mi equals 2 over 5, sehingga panjang sisi depan 2 dan panjang sisi miring 5.

Ditanyakan:

  • Nilai perbandingan trigonometri lainnya di kuadran I.

Penyelesaian:

Karena sudut a terletak di kuadran I, maka semua nilai trigonometri positif.

panjang sisi depan dan sisi miring telah diketahui, maka carilah dulu panjang sisi samping yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell panjang space sisi space samping end cell equals cell square root of panjang space sisi space miring squared minus panjang space sisi space depan squared end root end cell row blank equals cell square root of 5 squared minus 2 squared end root end cell row blank equals cell square root of 25 minus 4 end root end cell row blank equals cell square root of 21. end cell end table 

Setelah itu, perbandingan sisi trigonometri di kuadran I adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight a end cell equals cell sa over mi end cell row blank equals cell fraction numerator square root of 21 over denominator 5 end fraction. end cell row cell tan space straight a end cell equals cell de over sa end cell row blank equals cell fraction numerator 2 over denominator square root of 21 end fraction cross times fraction numerator square root of 21 over denominator square root of 21 end fraction equals 2 over 21 square root of 21. end cell row cell cosec space straight a end cell equals cell fraction numerator 1 over denominator sin space straight a end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled 2 over 5 end style end fraction end cell row blank equals cell 5 over 2. end cell row cell sec space straight a end cell equals cell fraction numerator 1 over denominator cos space straight a end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled fraction numerator square root of 21 over denominator 5 end fraction end style end fraction end cell row blank equals cell fraction numerator 5 over denominator square root of 21 end fraction cross times fraction numerator square root of 21 over denominator square root of 21 end fraction end cell row blank equals cell 5 over 21 square root of 21. end cell row cell cotan space straight a end cell equals cell fraction numerator 1 over denominator tan space straight a end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled fraction numerator 2 square root of 21 over denominator 21 end fraction end style end fraction end cell row blank equals cell fraction numerator 21 over denominator 2 square root of 21 end fraction cross times fraction numerator square root of 21 over denominator square root of 21 end fraction end cell row blank equals cell fraction numerator 21 square root of 21 over denominator 2 cross times 21 end fraction end cell row blank equals cell 1 half square root of 21. end cell end table   

Dengan demikian, itulah nilai-nilai perbandingan trigonometri di kuadran I.

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