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Jika , maka salah satu nilai  yang memenuhi adalah ....

Pertanyaan

Jika sin space left parenthesis 3 x minus 10 degree right parenthesis equals cos space left parenthesis x plus 20 degree right parenthesis, maka salah satu nilai x yang memenuhi adalah ....

  1. 20 degree 

  2. 35 degree 

  3. 40 degree 

  4. 50 degree 

  5. 60 degree 

Pembahasan Soal:

Ingat kembali rumus berikut.

  • sin space alpha equals cos space left parenthesis 90 degree minus alpha right parenthesis 
  • Jika diketahui cos space x equals cos space alpha maka

x equals alpha plus k times 360 degree atau x equals negative a plus k times 360 degree 

Dari rumus di atas, diperoleh perhitungan sebagai berikut.

 table attributes columnalign right center left columnspacing 0px end attributes row cell sin space left parenthesis 3 x minus 10 degree right parenthesis end cell equals cell cos space left parenthesis x plus 20 degree right parenthesis end cell row cell cos space open parentheses 90 degree minus open parentheses 3 x minus 10 degree close parentheses close parentheses end cell equals cell cos space left parenthesis x plus 20 degree right parenthesis end cell row cell cos space left parenthesis 90 degree minus 3 x plus 10 degree right parenthesis end cell equals cell cos space left parenthesis x plus 20 degree right parenthesis end cell row cell cos space left parenthesis 100 degree minus 3 x right parenthesis end cell equals cell cos space left parenthesis x plus 20 degree right parenthesis end cell end table 

Maka nilai x adalah 

begin mathsize 12px style x equals alpha plus k times 360 degree end style  begin mathsize 12px style x equals negative a plus k times 360 degree end style 
begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 100 degree minus 3 x right parenthesis end cell equals cell left parenthesis x plus 20 degree right parenthesis plus 0 times 360 degree end cell row cell 100 degree minus 3 x end cell equals cell x plus 20 degree end cell row cell negative 3 x minus x end cell equals cell 20 degree minus 100 degree end cell row cell negative 4 x end cell equals cell negative 80 degree end cell row x equals cell fraction numerator negative 80 degree over denominator negative 4 end fraction end cell row x equals cell 20 degree end cell end table end style  begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 100 degree minus 3 x right parenthesis end cell equals cell negative left parenthesis x plus 20 degree right parenthesis plus 0 times 360 degree end cell row cell 100 degree minus 3 x end cell equals cell negative x minus 20 degree end cell row cell negative 3 x plus x end cell equals cell negative 20 degree minus 100 degree end cell row cell negative 2 x end cell equals cell negative 120 degree end cell row x equals cell fraction numerator negative 120 degree over denominator negative 2 end fraction end cell row x equals cell 60 degree end cell end table end style 
begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 100 degree minus 3 x right parenthesis end cell equals cell left parenthesis x plus 20 degree right parenthesis plus 1 times 360 degree end cell row cell 100 degree minus 3 x end cell equals cell x plus 20 degree plus 360 degree end cell row cell negative 3 x minus x end cell equals cell 380 degree minus 100 degree end cell row cell negative 4 x end cell equals cell 280 degree end cell row x equals cell fraction numerator 280 degree over denominator negative 4 end fraction end cell row x equals cell negative 70 degree space left parenthesis TM right parenthesis end cell end table end style  begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 100 degree minus 3 x right parenthesis end cell equals cell negative left parenthesis x plus 20 degree right parenthesis plus 1 times 360 degree end cell row cell 100 degree minus 3 x end cell equals cell negative x minus 20 degree plus 360 degree end cell row cell negative 3 x plus x end cell equals cell 340 degree minus 100 degree end cell row cell negative 2 x end cell equals cell 240 degree end cell row x equals cell fraction numerator 240 degree over denominator negative 2 end fraction end cell row x equals cell negative 120 degree space left parenthesis TM right parenthesis end cell end table end style

Dengan demikian nilai x yang memenuhi adalah 20 degree dan 60 degree.

Jadi, jawaban yang benar adalah A dan E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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