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Pertanyaan

Buktikan: sin 1 8 ∘ = 4 − 1 + 5 ​ ​ .

Buktikan: .

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S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

terbukti .

terbukti sin space 18 degree equals fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction.

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Pembahasan

Ingat bahwa: Mencari : Misalkan: , maka: Jadi, terbukti .

Ingat bahwa:

  • sin space a equals cos space left parenthesis 90 degree minus a right parenthesis 
  • sin space 2 a equals 2 space sin space a space cos space a 
  • cos space 3 a equals 4 cos cubed a minus 3 cos space a 

Mencari sin space 18 degree:

Misalkan: theta equals 18 degree, maka:

 table attributes columnalign right center left columnspacing 0px end attributes row cell 5 theta end cell equals cell 90 degree end cell row cell 2 theta plus 3 theta end cell equals cell 90 degree end cell row cell 2 theta end cell equals cell 90 degree minus 3 theta end cell row cell sin 2 theta end cell equals cell sin left parenthesis 90 degree minus 3 theta right parenthesis equals cos 3 theta end cell row cell 2 sin theta cos theta end cell equals cell 4 cos cubed theta minus 3 cos theta end cell row cell 2 sin theta cos theta minus 4 cos cubed theta plus 3 cos theta end cell equals 0 row cell cos theta open parentheses 2 sin theta minus 4 cos squared theta plus 3 close parentheses end cell equals 0 row cell 2 sin theta minus 4 open parentheses 1 minus sin squared theta close parentheses plus 3 end cell equals 0 row cell sin theta end cell equals cell fraction numerator negative 2 plus-or-minus square root of 2 squared minus 4 cross times 4 cross times left parenthesis negative 1 right parenthesis end root over denominator 2 cross times 4 end fraction end cell row cell sin theta end cell equals cell fraction numerator negative 2 plus-or-minus square root of 20 over denominator 8 end fraction end cell row cell sin theta end cell equals cell fraction numerator square root of 5 minus 1 over denominator 4 end fraction end cell row cell sin space 18 degree end cell equals cell fraction numerator square root of 5 minus 1 over denominator 4 end fraction end cell end table  

Jadi, terbukti sin space 18 degree equals fraction numerator negative 1 plus square root of 5 over denominator 4 end fraction.

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