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Pernyataan berikut yang benar adalah ....

Pertanyaan

Pernyataan berikut yang benar adalah ....

  1. sin space 1 half theta equals plus-or-minus square root of fraction numerator 1 plus cos space theta over denominator 2 end fraction end root 

  2. sin space 1 half theta equals plus-or-minus square root of fraction numerator 1 plus 2 space cos space theta over denominator 2 end fraction end root 

  3. cos space 1 half theta equals plus-or-minus square root of fraction numerator 1 plus cos space theta over denominator 4 end fraction end root 

  4. cos space 1 half theta equals plus-or-minus square root of fraction numerator 2 space cos space theta minus 1 over denominator 2 end fraction end root 

  5. tan space 1 half theta equals plus-or-minus square root of fraction numerator 1 minus cos space theta over denominator cos space theta plus 1 end fraction end root 

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali sudut rangkap pada rumus trigonometri berikut.

  • cos space 2 A equals 1 minus 2 space sin squared space A 
  • cos space 2 A equals 2 space cos squared space A minus 1  

Misalkan A equals 1 half theta, maka diperoleh : 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 A end cell equals cell 1 minus 2 space sin squared space A end cell row cell cos space 2 open parentheses 1 half theta close parentheses end cell equals cell 1 minus 2 space sin squared space open parentheses 1 half theta close parentheses end cell row cell cos space theta end cell equals cell 1 minus 2 space sin squared space open parentheses 1 half theta close parentheses end cell row cell 2 space sin squared space open parentheses 1 half theta close parentheses end cell equals cell 1 minus cos space theta end cell row cell sin squared space open parentheses 1 half theta close parentheses end cell equals cell fraction numerator 1 minus cos space theta over denominator 2 end fraction end cell row cell sin space 1 half theta end cell equals cell plus-or-minus square root of fraction numerator 1 minus cos space theta over denominator 2 end fraction end root end cell end table 

 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 A end cell equals cell 2 space cos squared space A minus 1 end cell row cell cos space 2 open parentheses 1 half theta close parentheses end cell equals cell 2 space cos squared space open parentheses 1 half theta close parentheses minus 1 end cell row cell cos space theta end cell equals cell 2 space cos squared space open parentheses 1 half theta close parentheses minus 1 end cell row cell 2 space cos squared space open parentheses 1 half theta close parentheses end cell equals cell cos space theta plus 1 end cell row cell cos squared space open parentheses 1 half theta close parentheses end cell equals cell fraction numerator cos space theta plus 1 over denominator 2 end fraction end cell row cell cos space 1 half theta end cell equals cell plus-or-minus square root of fraction numerator cos space theta plus 1 over denominator 2 end fraction end root end cell end table 

Sehingga untuk tan space 1 half theta diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 1 half theta end cell equals cell fraction numerator sin space begin display style 1 half end style theta over denominator cos space begin display style 1 half end style theta end fraction end cell row blank equals cell plus-or-minus fraction numerator square root of begin display style fraction numerator 1 minus cos space theta over denominator 2 end fraction end style end root over denominator square root of begin display style fraction numerator cos space theta plus 1 over denominator 2 end fraction end style end root end fraction end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos space theta over denominator cos space theta plus 1 end fraction end root end cell end table 

Dengan demikian, pernyataan berikut yang benar adalah table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 1 half theta end cell equals cell plus-or-minus square root of fraction numerator 1 minus cos space theta over denominator cos space theta plus 1 end fraction end root end cell end table.

Oleh karena itu, jawaban yang benar adalah E.

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