Himpunan penyelesaian dari 2 sin 5x−3​=0 untuk 0∘≤x≤360∘ adalah...

Pertanyaan

Himpunan penyelesaian dari 2 space sin space 5 x minus square root of 3 equals 0 untuk 0 degree less or equal than x less or equal than 360 degree adalah...

  1. open curly brackets 12 degree comma space 24 degree comma space 74 degree comma space 96 degree comma space 146 degree comma space 178 degree comma space close curly brackets open curly brackets 238 degree comma space 240 degree comma space 300 degree comma space 312 degree close curly brackets 

  2. open curly brackets 12 degree comma space 54 degree comma space 84 degree comma space 96 degree comma space 156 degree comma space 168 degree comma space close curly brackets open curly brackets 238 degree comma space space 240 degree comma space 300 degree comma space 312 degree close curly brackets 

  3. open curly brackets 12 degree comma space 24 degree comma space 84 degree comma space 96 degree comma space 156 degree comma space 168 degree comma space close curly brackets open curly brackets 228 degree comma space 240 degree comma space 300 degree comma space 312 degree close curly brackets 

  4. open curly brackets 12 degree comma space 34 degree comma space 84 degree comma space 96 degree comma space 146 degree comma space 168 degree comma space close curly brackets open curly brackets 228 degree comma space 240 degree comma space 300 degree comma space 322 degree close curly brackets 

  5. open curly brackets 12 degree comma space 24 degree comma space 74 degree comma space 96 degree comma space 156 degree comma space 158 degree comma space close curly brackets open curly brackets 218 degree comma space 240 degree comma space 300 degree comma space 312 degree close curly brackets 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Persamaan Trigonometri Dasar

Penyelesaian persamaan trigonometri dasar bentuk sin space x equals a dilakukan dengan cara: mengubah bentuk sin space x equals a menjadi sin space x equals sin space a.

Ingat persamaan trigonometri dasar berikut:

Jika sin space x equals sin space alpha, nilai x equals alpha plus k times 360 degree atau x equals open parentheses 180 degree minus alpha close parentheses plus k times 360 degree.

2 space sin space 5 x minus square root of 3 equals 0 untuk 0 degree less or equal than x less or equal than 360 degree

Misal sin space 5 x equals p, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p minus square root of 3 end cell equals 0 row cell 2 p end cell equals cell square root of 3 end cell row p equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row blank equals cell 1 half square root of 3 end cell end table  

Karena  sin space 5 x equals p, maka:

sin space 5 x equals p sin space 5 x equals 1 half square root of 3 sin space 5 x equals sin space open parentheses 1 half square root of 3 close parentheses sin space 5 x equals sin space 60 degree  

Diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x end cell equals cell 60 degree plus k times 360 degree end cell row x equals cell fraction numerator up diagonal strike 5 open parentheses 12 degree plus k times 72 degree close parentheses over denominator up diagonal strike 5 end fraction end cell row blank equals cell 12 degree plus k times 72 degree end cell end table 

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x end cell equals cell open parentheses 180 degree minus 60 degree close parentheses plus k times 360 degree end cell row cell 5 x end cell equals cell 120 degree plus k times 360 degree end cell row x equals cell fraction numerator up diagonal strike 5 open parentheses 24 degree plus k times 72 degree close parentheses over denominator up diagonal strike 5 end fraction end cell row blank equals cell 24 degree plus k times 72 degree end cell end table 

Untuk k equals 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 12 degree plus 0 times 72 degree end cell row blank equals cell 12 degree end cell end table 

(Memenuhi)

atau 

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 24 degree plus 0 times 72 degree end cell row blank equals cell 24 degree end cell end table 

(Memenuhi)

Untuk k equals 1, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 12 degree plus 1 times 72 degree end cell row blank equals cell 12 degree plus 72 degree end cell row blank equals cell 84 degree end cell end table 

(Memenuhi)

atau

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 24 degree plus 1 times 72 degree end cell row blank equals cell 24 degree plus 72 degree end cell row blank equals cell 96 degree end cell end table 

(Memenuhi)

Untuk k equals 2, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 12 degree plus 2 times 72 degree end cell row blank equals cell 12 degree plus 144 degree end cell row blank equals cell 156 degree end cell end table 

(Memenuhi)

atau 

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 24 degree plus 2 times 72 degree end cell row blank equals cell 24 degree plus 144 degree end cell row blank equals cell 168 degree end cell end table 

(Memenuhi)

Untuk k equals 3, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 12 degree plus 3 times 72 degree end cell row blank equals cell 12 degree plus 216 degree end cell row blank equals cell 228 degree end cell end table

(Memenuhi)

atau 

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 24 degree plus 3 times 72 degree end cell row blank equals cell 24 degree plus 216 degree end cell row blank equals cell 240 degree end cell end table

(Memenuhi)

Untuk k equals 4, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 12 degree plus 4 times 72 degree end cell row blank equals cell 12 degree plus 288 degree end cell row blank equals cell 300 degree end cell end table 

(Memenuhi)

atau

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 24 degree plus 4 times 72 degree end cell row blank equals cell 24 degree plus 288 degree end cell row blank equals cell 312 degree end cell end table

(Memenuhi)

Dengan demikian, himpunan penyelesaiannya adalah open curly brackets 12 degree comma space 24 degree comma space 84 degree comma space 96 degree comma space 156 degree comma space 168 degree comma space close curly brackets open curly brackets 228 degree comma space 240 degree comma space 300 degree comma space 312 degree close curly brackets.

Oleh karena itu, jawaban yang benar adalah C.

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