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Himpunan penyelesaian persamaan  untuk  adalah ...

Himpunan penyelesaian persamaan square root of 2 space sin space 3 x equals 1 untuk 0 degree less or equal than x less or equal than 180 degree adalah ... 

  1. left curly bracket 15 degree comma space 45 degree comma space 135 degree comma space 175 degree right curly bracket 

  2. left curly bracket 15 degree comma space 45 degree comma space 135 degree comma space 165 degree right curly bracket 

  3. left curly bracket 35 degree comma space 45 degree comma space 165 degree right curly bracket  

  4. left curly bracket 35 degree comma space 45 degree comma space 145 degree right curly bracket 

  5. left curly bracket 35 degree comma space 45 degree comma space 135 degree right curly bracket 

Jawaban:

Diketahui square root of 2 space sin space 3 x equals 10 degree less or equal than x less or equal than 180 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 2 space sin space 3 straight x end cell equals 1 row cell sin space 3 straight x end cell equals cell fraction numerator 1 over denominator square root of 2 end fraction end cell row cell sin space 3 straight x end cell equals cell fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell sin space 3 straight x end cell equals cell 1 half square root of 2 end cell row cell sin space 3 straight x end cell equals cell sin space 45 degree end cell row cell 3 straight x end cell equals cell 45 degree end cell end table 

Dengan menggunakan rumus penyelesaian persamaan trigonometri untuk sinus yaitu jika sin space x degree equals sin space a degree maka left parenthesis i right parenthesis space x equals a plus k cross times 360 dan left parenthesis i i right parenthesis space x equals left parenthesis 180 minus a right parenthesis plus k cross times 360 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis i right parenthesis space x end cell equals cell a plus k cross times 360 end cell row cell 3 x end cell equals cell 45 plus k cross times 360 end cell row x equals cell 15 plus k cross times 120 end cell row blank blank blank row k equals cell 0 rightwards arrow x equals 15 plus 0 equals 15 degree end cell row k equals cell 1 rightwards arrow x equals 15 plus 1 cross times 120 space end cell row blank blank cell equals 15 plus 120 end cell row blank blank cell equals 135 degree end cell row k equals cell 2 rightwards arrow x equals 15 plus 2 cross times 120 end cell row blank blank cell equals 15 plus 240 end cell row blank blank cell equals 255 degree end cell end table 


   table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis i i right parenthesis space x end cell equals cell left parenthesis 180 minus a right parenthesis plus k cross times 360 end cell row cell 3 x end cell equals cell left parenthesis 180 minus 45 right parenthesis plus k cross times 360 end cell row cell 3 x end cell equals cell 135 plus k cross times 360 end cell row x equals cell 45 plus k cross times 120 end cell row blank blank blank row k equals cell 0 rightwards arrow x equals 45 plus 0 equals 45 degree end cell row k equals cell 1 rightwards arrow x equals 45 plus 1 cross times 120 end cell row blank blank cell equals 45 plus 120 equals 165 degree end cell row k equals cell 2 rightwards arrow x equals 45 plus 2 cross times 120 end cell row blank blank cell equals 45 plus 240 equals 285 degree end cell end table  

Himpunan penyelesaiannya yaitu left curly bracket 15 degree comma space 45 degree comma space 135 degree comma space 165 degree right curly bracket 

Oleh karena itu, jawaban yang benar adalah B.space 

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