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Diketahui siku-siku di . Jika , maka nilai

Diketahui begin mathsize 14px style triangle ABC end style siku-siku di begin mathsize 14px style straight C end style. Jika begin mathsize 14px style sin space straight B equals p end style, maka nilai begin mathsize 14px style tan space straight B equals space... end style 

  1. begin mathsize 14px style fraction numerator p over denominator square root of 1 minus p squared end root end fraction end style 

  2. begin mathsize 14px style fraction numerator 1 over denominator square root of 1 minus p squared end root end fraction end style 

  3. begin mathsize 14px style fraction numerator 1 over denominator square root of p squared minus 1 end root end fraction end style 

  4. begin mathsize 14px style fraction numerator p over denominator square root of p squared minus 1 end root end fraction end style 

  5. begin mathsize 14px style fraction numerator square root of 1 minus p squared end root over denominator p end fraction end style 

Jawaban:

Karena begin mathsize 14px style sin space straight B equals p end style, maka dapat ditulis 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space B end cell equals cell fraction numerator panjang space sisi space depan space B over denominator panjang space sisi space miring end fraction end cell row p equals cell fraction numerator panjang space sisi space depan space B over denominator panjang space sisi space miring end fraction end cell row cell p over 1 end cell equals cell fraction numerator panjang space sisi space depan space B over denominator panjang space sisi space miring end fraction end cell end table end style 

Jadi panjang sisi depan sudut begin mathsize 14px style B end style adalah begin mathsize 14px style p end style dan panjang sisi miring begin mathsize 14px style 1 space end stylesehingga segitiga ABC tersebut dapat digambarkan seperti berikut ini 


 


Dengan menggunakan teorema Pythagoras diperoleh 

begin mathsize 14px style BC equals square root of AC squared minus AC squared end root BC equals square root of 1 squared minus p to the power of italic 2 end root end style 

Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space B end cell equals cell fraction numerator A C over denominator B C end fraction end cell row blank equals cell fraction numerator p over denominator square root of 1 minus p squared end root end fraction end cell end table end style 

Jadi jawaban yang tepat adalah A.

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