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Hitunglah: sin 52∘ sin 68∘−sin 13∘ sin 47∘−sin 9∘ sin 25∘

Pertanyaan

Hitunglah:

sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

 nilai dari sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree adalah 1 half.

Pembahasan

Ingat bahwa: 

  • 2 space sin space a space sin space b equals negative cos space left parenthesis a plus b right parenthesis plus cos space left parenthesis a minus b right parenthesis 

Mencari nilai dari sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree, Didapat:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses minus sin open parentheses 9 degree close parentheses sin open parentheses 25 degree close parentheses end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 9 degree plus 25 degree close parentheses plus cos open parentheses 9 degree minus 25 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses negative 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 13 degree plus 47 degree close parentheses plus cos open parentheses 13 degree minus 47 degree close parentheses over denominator 2 end fraction end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses end cell row blank blank cell plus fraction numerator cos open parentheses 60 degree close parentheses minus cos open parentheses 34 degree close parentheses plus cos open parentheses 34 degree close parentheses minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator cos open parentheses 60 degree close parentheses minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator 1 half minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 52 degree plus 68 degree close parentheses plus cos open parentheses 52 degree minus 68 degree close parentheses over denominator 2 end fraction end cell row blank blank cell plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 120 degree close parentheses plus cos open parentheses negative 16 degree close parentheses over denominator 2 end fraction plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 120 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 2 open parentheses negative 1 half close parentheses plus 1 over denominator 4 end fraction end cell row blank equals cell 1 half end cell end table  

Jadi, nilai dari sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree adalah 1 half.

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