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Sinus 12∘=…   (Diketahui sin 18∘=4−1+5​​)

Pertanyaan

begin mathsize 14px style Sinus space 12 degree equals horizontal ellipsis space end style 
(Diketahui begin mathsize 14px style sin space 18 degree equals fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction end style)

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R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style sin space 12 degree equals 1 over 8 open parentheses square root of 10 plus 2 square root of 5 end root plus square root of 3 minus square root of 15 close parentheses end style.

Pembahasan

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Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 18 degree end cell equals cell square root of 1 minus open parentheses fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction close parentheses squared end root end cell row blank equals cell square root of 1 minus fraction numerator left parenthesis 1 minus 2 square root of 5 plus 5 right parenthesis over denominator 16 end fraction end root end cell row blank equals cell square root of fraction numerator 16 minus 6 plus 2 square root of 5 over denominator 16 end fraction end root end cell row blank equals cell 1 fourth square root of 10 plus 2 square root of 5 end root end cell end table end style 

Karena sudutnya berada di Kuadran I, maka hasil akar yang diambil yang positif.

Ingat: 

begin mathsize 14px style sin open parentheses alpha minus beta close parentheses equals sin space alpha space times cos space beta minus cos space alpha space times sin space beta end style 

Sehingga

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 12 degree end cell equals cell sin open parentheses 30 degree minus 18 degree close parentheses end cell row blank equals cell sin space 30 degree times cos space 18 degree minus cos space 30 degree times sin space 18 degree end cell row blank equals cell 1 half times fraction numerator square root of 10 plus 2 square root of 5 end root over denominator 4 end fraction minus 1 half square root of 3 times fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction end cell row blank equals cell 1 over 8 open parentheses square root of 10 plus 2 square root of 5 end root plus square root of 3 minus square root of 15 close parentheses end cell end table end style 

Jadi, nilai begin mathsize 14px style sin space 12 degree equals 1 over 8 open parentheses square root of 10 plus 2 square root of 5 end root plus square root of 3 minus square root of 15 close parentheses end style.

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