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Himpunan penyelesaian persamaan  pada interval  adalah ....

Pertanyaan

Himpunan penyelesaian persamaan sin space open parentheses 3 x plus 30 degree close parentheses equals 1 half square root of 2 pada interval 0 degree less or equal than x less or equal than 180 degree adalah ....

  1. open curly brackets 5 degree comma 35 degree close curly brackets

  2. open curly brackets 5 degree comma 125 degree close curly brackets

  3. open curly brackets 5 degree comma 35 degree comma 65 degree comma 95 degree close curly brackets

  4. open curly brackets 5 degree comma 35 degree comma 125 degree comma 155 degree close curly brackets

  5. open curly brackets 5 degree comma 35 degree comma 95 degree comma 155 degree close curly brackets

Pembahasan Soal:

Untuk persamaan trigonometri bentuk sin, berlaku:

sin space x equals sin space alpha

dengan

x equals alpha plus k times 360 degree dan x equals open parentheses 180 degree minus alpha close parentheses plus k times 360 degree

sin space open parentheses 3 x plus 30 degree close parentheses equals 1 half square root of 2 sin space open parentheses 3 x plus 30 degree close parentheses equals sin space 45 degree

diperoleh

3 x plus 30 degree equals 45 degree plus k.360 degree

  • Untuk k equals 0

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 45 degree end cell row cell 3 x end cell equals cell 15 degree end cell row x equals cell 5 degree end cell end table

  • Untuk k equals 1

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 45 degree plus 360 degree end cell row cell 3 x end cell equals cell 137 degree end cell row x equals cell 125 degree end cell end table

  • Untuk k equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 45 degree plus 720 degree end cell row cell 3 x end cell equals cell 735 degree end cell row x equals cell 245 degree end cell end table

(Tidak termasuk, karena di luar interval 0 degree less than x less than 180 degree)

3 x plus 30 degree equals left parenthesis 180 degree minus 45 degree right parenthesis plus k.360 degree

  • Untuk k equals 0

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 135 degree end cell row cell 3 x end cell equals cell 105 degree end cell row x equals cell 35 degree end cell end table

  • Untuk k equals 1

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 135 degree plus 360 degree end cell row cell 3 x end cell equals cell 465 degree end cell row x equals cell 155 degree end cell end table

  • Untuk k equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 30 degree end cell equals cell 135 degree plus 720 degree end cell row cell 3 x end cell equals cell 825 degree end cell row x equals cell 275 degree end cell end table

(Tidak termasuk, karena di luar interval 0 degree less than x less than 180 degree)

Jadi, himpunan penyelesaiannya yaitu open curly brackets 5 degree comma 35 degree comma 125 degree comma 155 degree close curly brackets.

Jadi, jawaban yang tepat adalah D.
 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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