Himpunan penyelesaian dari sin 4x=−21​3​ untuk 0∘≤x≤360∘ adalah ....

Pertanyaan

Himpunan penyelesaian dari sin space 4 x equals negative 1 half square root of 3 untuk 0 degree less or equal than x less or equal than 360 degree adalah ....

  1. left curly bracket 30 degree comma space 75 degree comma space 120 degree comma space 165 degree comma space 240 degree comma space 255 degree comma space 330 degree comma space space 345 degree right curly bracket

  2. left curly bracket 30 degree comma space 75 degree comma space 150 degree comma space 165 degree comma space 210 degree comma space 255 degree comma space 300 degree comma space 345 degree right curly bracket

  3. left curly bracket 60 degree comma space 75 degree comma space 150 degree comma space 165 degree comma space 240 degree comma space 255 degree comma space 330 degree comma space 345 degree right curly bracket

  4. left curly bracket 60 degree comma space 75 degree comma space 120 degree comma space 165 degree comma space 210 degree comma space 255 degree comma space 330 degree comma space 345 degree right curly bracket

  5. left curly bracket 60 degree comma space 75 degree comma space 150 degree comma space 175 degree comma space 240 degree comma space 265 degree comma space 330 degree comma space 345 degree right curly bracket  

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Ingat 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

Diketahu sin space 4 x equals negative 1 half square root of 3 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 sin space 4 x end cell equals cell negative 1 half square root of 3 space left parenthesis straight K italic. italic space III divided by IV right parenthesis end cell row blank equals cell sin space left parenthesis 180 degree plus 60 degree right parenthesis end cell row cell sin space 4 x end cell equals cell sin space 240 degree end cell end table 

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 4 bold x end cell bold equals cell bold 240 bold degree bold plus bold k bold times bold 360 bold degree end cell row straight x equals cell 60 degree plus straight k times 90 degree end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row k equals cell 0 comma space x equals 60 degree plus 0 times 90 degree equals 60 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 1 comma space x equals 60 degree plus 1 times 90 degree equals 150 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 2 comma space x equals 60 degree plus 2 times 90 degree equals 240 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 3 comma space x equals 60 degree plus 3 times 90 degree equals 330 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 4 comma space x equals 60 degree plus 4 times 90 degree equals 420 degree space left parenthesis tidak space memenuhi right parenthesis end cell end table

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 4 bold italic x end cell bold equals cell bold left parenthesis bold 180 bold degree bold minus bold 240 bold degree bold right parenthesis bold plus bold italic k bold times bold 360 bold degree end cell row cell 4 x end cell equals cell negative 60 degree plus k times 360 degree end cell row x equals cell negative 15 degree plus k times 90 degree end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row k equals cell 0 comma space x equals negative 15 degree plus 0 times 90 degree equals negative 15 degree space left parenthesis tidak space memenuhi right parenthesis end cell row k equals cell 1 comma space x equals negative 15 degree plus 1 times 90 degree equals 75 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 2 comma space x equals negative 15 degree plus 2 times 90 degree equals 165 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 3 comma space x equals negative 15 degree plus 3 times 90 degree equals 255 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 4 comma space x equals negative 15 degree plus 4 times 90 degree equals 345 degree space left parenthesis memenuhi right parenthesis end cell row k equals cell 5 comma space x equals negative 15 degree plus 5 times 90 degree equals 435 degree space left parenthesis tidak space memenuhi right parenthesis end cell end table

Jadi, himpunan penyelesaiannya adalah left curly bracket 60 degree comma space 75 degree comma space 150 degree comma space 165 degree comma space 240 degree comma space 255 degree comma space 330 degree comma space 345 degree right curly bracket.

Oleh karena itu, jawaban yang benar adalah C.

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