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Himpunan penyelesaian dari persamaan begin mathsize 12px style 2 cos squared x plus 5 sin x minus 4 equals 0 end style untuk begin mathsize 12px style 0 degree less or equal than x less or equal than 360 degree end style adalah...

  1. begin mathsize 12px style open curly brackets 30 degree comma space 150 degree close curly brackets end style

  2. begin mathsize 12px style open curly brackets 30 degree comma space 300 degree close curly brackets end style

  3. begin mathsize 12px style open curly brackets 60 degree comma space 150 degree close curly brackets end style

  4. begin mathsize 12px style open curly brackets 60 degree comma space 300 degree close curly brackets end style

  5. begin mathsize 12px style open curly brackets 150 degree comma space 300 degree close curly brackets end style

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

begin mathsize 12px style cos squared x plus sin squared x equals 1 end style

begin mathsize 12px style sin x equals sin alpha end style memiliki penyelesaian:

  • begin mathsize 12px style x subscript 1 equals alpha plus k times 360 degree end style atau
  • begin mathsize 12px style x subscript 2 equals open parentheses 180 minus alpha close parentheses plus k times 360 degree end style

begin mathsize 12px style 2 cos squared x plus 5 sin x minus 4 equals 0 end style untuk begin mathsize 12px style 0 degree less or equal than x less or equal than 360 degree end style

begin mathsize 12px style 2 cos squared x plus 5 sin x minus 4 equals 0  2 open parentheses 1 minus sin squared x close parentheses plus 5 sin x minus 4 equals 0  2 minus 2 sin squared x plus 5 sin x minus 4 equals 0  2 sin squared x minus 5 sin x plus 2 equals 0  open parentheses 2 space sin x minus 1 close parentheses open parentheses sin x minus 2 close parentheses equals 0 end style

Pembuat nol fungsi:

begin mathsize 12px style 2 space sin x minus 1 equals 0 end style atau begin mathsize 12px style sin x minus 2 equals 0 end style

begin mathsize 12px style sin x equals 1 half end style (memenuhi) atau sin x = 2 (tidak memenuhi) sehingga persamaan trigonometrinya:

begin mathsize 12px style sin x equals 1 half  sin x equals sin space 30 degree end style

Penyelesaian:

begin mathsize 12px style x subscript 1 equals 30 degree plus k times 360 degree end style atau begin mathsize 12px style x subscript 2 equals open parentheses 180 minus 30 close parentheses plus k times 360 degree end style

begin mathsize 12px style x subscript 1 equals 30 degree plus k times 360 degree end style atau begin mathsize 12px style x subscript 2 equals 150 degree plus k times 360 degree end style

Untuk k = 0 diperoleh:

begin mathsize 12px style x subscript 1 equals 30 degree end style atau begin mathsize 12px style x subscript 2 equals 150 degree end style

Jadi, himpunan penyelesaiannya adalah begin mathsize 12px style open curly brackets 30 degree comma space 150 degree close curly brackets end style

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5.0 (3 rating)

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