Diketahui sin α=p+1p​, hitunglah cos α, tan α, sec α, cosec α, dan cotan α!

Pertanyaan

Diketahui begin mathsize 14px style sin space alpha equals fraction numerator p over denominator p plus 1 end fraction end style, hitunglah begin mathsize 14px style cos space alpha end style, begin mathsize 14px style tan space alpha end style, begin mathsize 14px style sec space straight alpha end style, begin mathsize 14px style cosec space straight alpha end style, dan begin mathsize 14px style cotan space straight alpha end style!

 

S. Luke

Master Teacher

Jawaban terverifikasi

Pembahasan

Karena diketahui begin mathsize 14px style sin space alpha end style, maka didapat hubungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell depan over miring end cell row blank equals cell fraction numerator p over denominator p plus 1 end fraction end cell end table

Sebelum mencari yang ditanyakan, terlebih dahulu kita menentukan panjang sisi samping segitiga menggunakan Teorema Pythagoras berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell square root of left parenthesis p plus 1 right parenthesis squared minus p squared end root end cell row blank equals cell square root of p squared plus 2 p plus 1 minus p squared end root end cell row x equals cell square root of 2 p plus 1 end root end cell end table end style

Jadi, panjang sisi samping segitiga adalah begin mathsize 14px style square root of 2 p plus 1 end root end style.

Selanjutnya, nilai dari begin mathsize 14px style cos space alpha end style, begin mathsize 14px style tan space alpha end style, begin mathsize 14px style sec space straight alpha end style, begin mathsize 14px style cosec space straight alpha end style, dan begin mathsize 14px style cotan space straight alpha end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight alpha end cell equals cell samping over miring end cell row blank equals cell fraction numerator square root of 2 p plus 1 end root over denominator p plus 1 end fraction end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight alpha end cell equals cell depan over samping end cell row blank equals cell fraction numerator straight p over denominator square root of 2 straight p plus 1 end root end fraction end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s e c space straight alpha end cell equals cell 1 over cos end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 2 p plus 1 end root over denominator p plus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator p plus 1 over denominator square root of 2 p plus 1 end root end fraction end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cosec space straight alpha end cell equals cell 1 over sin end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator p over denominator p plus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator p plus 1 over denominator p end fraction end cell end table end style

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79

5.0 (2 rating)

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