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Himpunan penyelesaian dari persamaan cos 2 x − 3 ​ sin x ⋅ cos x + 2 sin 2 x − 2 = 0 untuk 0 ∘ ≤ x ≤ 36 0 ∘ adalah...

Himpunan penyelesaian dari persamaan  untuk  adalah...

  1. open curly brackets 0 degree comma space 30 degree comma space 180 degree comma space 210 degree comma space 360 degree close curly brackets

  2. open curly brackets 0 degree comma space 30 degree comma space 180 degree comma space 270 degree comma space 360 degree close curly brackets

  3. open curly brackets 90 degree comma space 120 degree comma space 270 degree comma space 300 degree close curly brackets

  4. open curly brackets 90 degree comma space 150 degree comma space 240 degree comma space 210 degree comma space 300 degree close curly brackets

  5. open curly brackets 90 degree comma space 150 degree comma space 270 degree comma space 330 degree close curly brackets

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N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

jawaban yang benar adalah E.

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Pembahasan

Pembahasan
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Dengan menggunakan konsep trigonometri, diperoleh: Menggunakan rumus , dimana Kemudian, Dengan demikian, Oleh karena itu, jawaban yang benar adalah E.

Dengan menggunakan konsep trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared x minus square root of 3 sin space x times cos space x plus 2 sin squared x minus 2 end cell equals 0 row cell open parentheses 1 minus sin squared x close parentheses minus fraction numerator square root of 3 over denominator 2 end fraction 2 sin space x times cos space x plus 2 sin squared x minus 2 end cell equals 0 row cell open parentheses fraction numerator 1 over denominator negative 2 end fraction close parentheses minus 2 sin squared x minus fraction numerator square root of 3 over denominator 2 end fraction sin space 2 x minus 1 end cell equals 0 row cell fraction numerator 1 over denominator negative 2 end fraction open parentheses cos space 2 x minus 1 close parentheses minus fraction numerator square root of 3 over denominator 2 end fraction sin space 2 x minus 1 end cell equals 0 row cell negative cos space 2 x plus 1 minus square root of 3 sin space 2 x minus 2 end cell equals 0 row cell negative cos space 2 x minus square root of 3 sin 2 x end cell equals 1 row cell cos space 2 x plus square root of 3 sin 2 x end cell equals 1 end table

Menggunakan rumus k cos open parentheses x minus alpha close parentheses equals c, dimana a equals 1 comma space b equals square root of 3 comma space c equals negative 1 comma

table attributes columnalign right center left columnspacing 0px end attributes row k equals cell square root of 1 squared plus left parenthesis square root of 3 right parenthesis squared end root equals 2 end cell row cell tan alpha end cell equals cell fraction numerator square root of 3 over denominator 1 end fraction equals square root of 3 end cell row alpha equals cell 60 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 cos space left parenthesis 2 x minus 60 right parenthesis degree equals negative 1 end cell row blank left right double arrow cell cos space left parenthesis 2 x minus 60 right parenthesis degree equals negative 1 half end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x minus 60 right parenthesis degree end cell equals cell negative 1 half end cell row cell cos space left parenthesis 2 x minus 60 right parenthesis degree end cell equals cell cos space 120 degree end cell row cell space 2 x minus 60 degree end cell equals cell plus-or-minus 120 degree plus n times 360 degree end cell row cell 2 x subscript 1 minus 60 degree end cell equals cell 120 degree plus n times 360 degree end cell row cell 2 x subscript 1 end cell equals cell 180 degree plus n times 360 degree end cell row cell x subscript 1 end cell equals cell 90 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row cell x subscript 1 end cell equals cell 90 degree plus 0 times 180 degree end cell row blank equals cell 90 degree end cell row cell x subscript 1 end cell equals cell 90 degree plus 1 times 180 degree end cell row blank equals cell 270 degree end cell row cell x subscript 1 end cell equals cell 90 degree plus 2 times 180 degree end cell row blank equals cell 450 degree space left parenthesis tidak space memenuhi right parenthesis end cell row cell atau space 2 x subscript 2 minus 60 degree end cell equals cell negative 120 degree plus n times 360 degree end cell row cell 2 x subscript 2 end cell equals cell negative 60 degree plus n times 360 degree end cell row cell x subscript 2 end cell equals cell negative 30 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row cell x subscript 2 end cell equals cell negative 30 degree plus 0 times 180 degree end cell row blank equals cell negative 30 degree space left parenthesis tidak space memenuhi right parenthesis end cell row cell x subscript 2 end cell equals cell negative 30 degree plus 1 times 180 degree end cell row blank equals cell 150 degree end cell row cell x subscript 2 end cell equals cell negative 30 degree plus 2 times 180 degree end cell row blank equals cell 330 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 90 degree comma space 150 degree comma space 270 degree comma space 330 degree close curly brackets end cell end table


Oleh karena itu, jawaban yang benar adalah E.

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