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Himpunan penyelesaian dari 2 sin23x−sin 3x+1=0 untuk 0∘≤x≤360∘ adalah ....

Pertanyaan

Himpunan penyelesaian dari 2 space sin squared 3 x minus sin space 3 x plus 1 equals 0 untuk 0 degree less or equal than x less or equal than 360 degree adalah ....

  1. left curly bracket 30 degree comma space 70 degree comma space 110 degree comma space 120 degree comma space 190 degree comma space space 230 degree comma space 300 degree comma space 310 degree comma space 350 degree right curly bracket

  2. left curly bracket 30 degree comma space 70 degree comma space 110 degree comma space 150 degree comma space 190 degree comma space space 230 degree comma space 270 degree comma space 310 degree comma space 350 degree right curly bracket

  3. left curly bracket 60 degree comma space 70 degree comma space 110 degree comma space 120 degree comma space 190 degree comma space 230 degree comma space 270 degree comma space 300 degree comma space 350 degree right curly bracket

  4. left curly bracket 30 degree comma space 80 degree comma space 110 degree comma space 170 degree comma space 190 degree comma space 230 degree comma space 270 degree comma space 310 degree comma space 350 degree right curly bracket

  5. left curly bracket 60 degree comma space 110 degree comma space 150 degree comma space 170 degree comma space 230 degree comma space 270 degree comma space 330 degree comma space 350 degree right curly bracket  

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah B.

Penyelesaian persamaan trigonometri bentuk persamaan kuadrat dilakukan dengan memfaktorkan terlebih dahulu.

Didapatkan sin space x equals a diubah dahulu menjadi sin space x equals sin space alpha.

Jika sin space x equals sin space alpha, maka

  • x equals alpha plus k times 360 degree
  • x equals left parenthesis 180 degree minus alpha right parenthesis plus k times 360 degree

Diketahui 2 space sin squared 3 x minus sin space 3 x plus 1 equals 0 untuk 0 degree less or equal than x less or equal than 360 degree, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin squared 3 x minus sin space 3 x plus 1 end cell equals 0 row cell left parenthesis 2 space sin space 3 x plus 1 right parenthesis left parenthesis sin space 3 x minus 1 right parenthesis end cell equals 0 end table

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space 3 x plus 1 end cell equals 0 row cell 2 space sin space 3 x end cell equals cell negative 1 end cell row cell sin space 3 x end cell equals cell negative 1 half space left parenthesis straight K. space III divided by IV right parenthesis end cell row blank equals cell sin space left parenthesis 180 degree plus 30 right parenthesis end cell row cell sin space 3 straight x end cell equals cell sin space 210 degree end cell end table end style  atau  table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 3 x minus 1 end cell equals 0 row cell sin space 3 x end cell equals 1 row cell sin space 3 x end cell equals cell sin space 90 degree end cell end table

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 3 bold italic x end cell bold equals cell bold 210 bold degree bold plus bold italic k bold times bold 360 bold degree end cell row x equals cell 70 degree plus k times 120 degree end cell end table

k equals 0 comma space x equals 70 degree plus 0 times 120 degree equals 70 degree space left parenthesis memenuhi right parenthesis k equals 1 comma space x equals 70 degree plus 1 times 120 degree equals 190 degree space left parenthesis memenuhi right parenthesis k equals 2 comma space x equals 70 degree plus 2 times 120 degree equals 310 degree space left parenthesis memenuhi right parenthesis k equals 3 comma space x equals 70 degree plus 3 times 120 degree equals 430 degree space left parenthesis tidak space memenuhi right parenthesis

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 3 bold italic x end cell bold equals cell bold left parenthesis bold 180 bold degree bold minus bold 210 bold degree bold right parenthesis bold plus bold italic k bold times bold 360 bold degree end cell row cell 3 x end cell equals cell negative 30 degree plus k times 360 degree end cell row x equals cell negative 10 degree plus k times 120 degree end cell end table

k equals 0 comma space x equals negative 10 degree plus 0 times 120 degree equals negative 10 degree space left parenthesis tidak space memenuhi right parenthesis k equals 1 comma space x equals negative 10 degree plus 1 times 120 degree equals 110 degree space left parenthesis memenuhi right parenthesis k equals 2 comma space x equals negative 10 degree plus 2 times 120 degree equals 230 degree space left parenthesis memenuhi right parenthesis k equals 3 comma space x equals negative 10 degree plus 3 times 120 degree equals 350 degree space left parenthesis memenuhi right parenthesis k equals 4 comma space x equals negative 10 degree plus 4 times 120 degree equals 470 degree space left parenthesis tidak space memenuhi right parenthesis

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 3 bold italic x end cell bold equals cell bold 90 bold degree bold plus bold italic k bold times bold 360 bold degree end cell row x equals cell 30 degree plus k times 120 degree end cell end table

k equals 0 comma space x equals 30 degree plus 0 times 120 degree equals 30 degree space left parenthesis memenuhi right parenthesis k equals 1 comma space x equals 30 degree plus 1 times 120 degree equals 150 degree space left parenthesis memenuhi right parenthesis k equals 2 comma space x equals 30 degree plus 3 times 120 degree equals 390 degree space left parenthesis tidak space memenuhi right parenthesis

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 3 bold italic x end cell bold equals cell bold left parenthesis bold 180 bold degree bold minus bold 90 bold degree bold right parenthesis bold plus bold italic k bold times bold 360 bold degree end cell row cell 3 x end cell equals cell 90 degree plus k times 360 degree end cell row x equals cell 30 degree plus k times 120 degree rightwards arrow space penyelesaian space sama end cell end table

Jadi, himpunan penyelesaiannya adalahleft curly bracket 30 degree comma space 70 degree comma space 110 degree comma space 150 degree comma space 190 degree comma space space 230 degree comma space 270 degree comma space 310 degree comma space 350 degree right curly bracket.

Oleh karena itu, jawaban yang benar adalah B.

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