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Jika begin mathsize 14px style sin space sin space 3 degree equals a end style, maka begin mathsize 14px style cos space cos space 39 degree equals... end style.

  1. begin mathsize 14px style 1 half square root of 2 open parentheses open parentheses 1 minus 2 a squared close parentheses minus 2 a square root of 1 minus a squared end root close parentheses end style 

  2. begin mathsize 14px style 1 half square root of 2 open parentheses open parentheses 1 plus 2 a squared close parentheses minus 2 a square root of 1 plus a squared end root close parentheses end style 

  3. begin mathsize 14px style 1 half square root of 2 open parentheses open parentheses 1 minus 2 a squared close parentheses plus 2 a square root of 1 plus a squared end root close parentheses end style 

  4. begin mathsize 14px style 1 half square root of 2 open parentheses open parentheses 1 minus 2 a squared close parentheses plus 2 a square root of 1 minus a squared end root close parentheses end style 

  5. begin mathsize 14px style 1 half square root of 2 open parentheses open parentheses 1 plus plus 2 a squared close parentheses plus 2 a square root of 1 plus a squared end root close parentheses end style 

Pembahasan Soal:

Gunakan konsep jumlah dua sudut pada sinus

Diketahui soal jika begin mathsize 14px style sin space sin space 3 degree equals a end style, maka begin mathsize 14px style cos space cos space 39 degree equals... end style.

Agar soal dapat diselesaikan asumsikan bahwa begin mathsize 14px style sin space sin space 3 degree equals a end style adalah begin mathsize 14px style sin space 3 degree equals a end style dan yang akan ditentukan adalah begin mathsize 14px style cos space 39 degree end style.

Gunakan perhitungan teorema Pythagoras dan perbandingan sisi trigonometri, begin mathsize 14px style sin space 3 degree equals a end style artinya sisi depannya adalah begin mathsize 14px style a end style, sisi miringnya adalah begin mathsize 14px style 1 end style dan sisi dekatnya adalah begin mathsize 14px style square root of 1 minus a squared end root end style.

begin mathsize 14px style cos space 3 degree equals fraction numerator square root of 1 minus a squared end root over denominator 1 end fraction equals square root of 1 minus a squared end root end style

Menentukan nilai begin mathsize 14px style sin space 6 degree end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 3 degree end cell equals a row cell sin space open parentheses 2 cross times 3 degree close parentheses end cell equals cell 2 space sin space 3 degree space cos space 3 degree end cell row cell sin space 6 degree end cell equals cell 2 a square root of 1 minus a squared end root end cell end table end style 

Diperoleh nilai begin mathsize 14px style sin space 6 degree equals 2 a square root of 1 minus a squared end root end style, kemudian tentukan begin mathsize 14px style cos space 6 degree end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cos space 2 x end cell equals cell 1 minus 2 space sin squared space x end cell row cell cos space 6 degree end cell equals cell 1 minus 2 space sin squared space 3 degree end cell row cell cos space 6 degree end cell equals cell 1 minus 2 a squared end cell end table end style 

Diperoleh nilai begin mathsize 14px style cos space 6 degree equals 1 minus 2 a squared end style, sehingga nilai begin mathsize 14px style cos space 39 degree end style dapat dihitung sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cos space open parentheses straight A minus straight B close parentheses end cell equals cell cos space straight A space cos space straight B plus sin space straight A space sin space straight B end cell row cell cos space 39 degree end cell equals cell cos space open parentheses 45 degree minus 6 degree close parentheses end cell row blank equals cell cos space 45 degree cos space 6 degree plus sin space 45 degree space sin space 6 degree end cell row blank equals cell 1 half square root of 2 open parentheses 1 minus 2 a squared close parentheses plus 1 half square root of 2 open parentheses 2 a square root of 1 minus a squared end root close parentheses end cell row cell cos space 39 degree end cell equals cell 1 half square root of 2 open parentheses open parentheses 1 minus 2 a squared close parentheses plus open parentheses 2 a square root of 1 minus a squared end root close parentheses close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 April 2021

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