Jika 2π​≤x≤23π​ memenuhi 2 sin x1−4 cos x​+1−cos x2 sin x​=7, maka nilai cos x = ....

Pertanyaan

Jika straight pi over 2 less or equal than x less or equal than fraction numerator 3 straight pi over denominator 2 end fraction memenuhi fraction numerator 1 minus 4 space cos space x over denominator 2 space sin space x end fraction plus fraction numerator 2 space sin space x over denominator 1 minus cos space x end fraction equals 7, maka nilai cos space x = ....

  1. 0 

  2. table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 171 over denominator 14 end fraction end cell end table 

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 131 over denominator 14 end fraction end cell end table 

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 171 over denominator 14 end fraction end cell end table 

  5. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 131 over denominator 14 end fraction end cell end table 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat kembali identitas dasar trigonometri.

sin squared space x plus cos squared space x equals 1

dan perbandingan sisi pada trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell depan over miring end cell row cell cos space x end cell equals cell samping over miring end cell end table

Memenuhi persamaan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 minus 4 space cos space x over denominator 2 space sin space x end fraction plus fraction numerator 2 space sin space x over denominator 1 minus cos space x end fraction end cell equals 7 row cell fraction numerator open parentheses 1 minus 4 space cos space x close parentheses open parentheses 1 minus cos space x close parentheses plus 4 space sin squared space x over denominator open parentheses 1 minus cos space x close parentheses 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 1 plus 4 space cos squared space x minus 5 space cos space x plus 4 space sin squared space x over denominator open parentheses 1 minus cos space x close parentheses 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 1 minus 5 space cos space x plus 4 open parentheses sin squared space x plus cos squared space x close parentheses over denominator open parentheses 1 minus cos space x close parentheses 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 1 minus 5 space cos space x plus 4 open parentheses 1 close parentheses over denominator open parentheses 1 minus cos space x close parentheses 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 5 minus 5 space cos space x over denominator open parentheses 1 minus cos space x close parentheses 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 5 up diagonal strike open parentheses 1 minus cos space x close parentheses end strike over denominator up diagonal strike open parentheses 1 minus cos space x close parentheses end strike 2 space sin space x end fraction end cell equals 7 row cell fraction numerator 5 over denominator 2 space sin space x end fraction end cell equals 7 row cell sin space x end cell equals cell 5 over 14 end cell end table

straight pi over 2 less or equal than x less or equal than fraction numerator 3 straight pi over denominator 2 end fractionx berada dikuadran II maka cos bernilai negatif.

sin space x equals 5 over 14 equals de over mi

table attributes columnalign right center left columnspacing 0px end attributes row sa equals cell square root of mi squared minus de squared end root end cell row blank equals cell square root of 14 squared minus 5 squared end root end cell row blank equals cell square root of 196 minus 25 end root end cell row blank equals cell square root of 171 end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell negative sa over mi end cell row blank equals cell negative fraction numerator square root of 171 over denominator 14 end fraction end cell end table

Dengan demikian, nilai cos space x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 171 over denominator 14 end fraction end cell end table.

Oleh karena itu, jawaban yang benar adalah B.

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