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Himpunan penyelesaian dari cos (x+45)∘+cos (x−45∘)=2​ untuk 0∘<x<360∘. Nilai sin x=...

Pertanyaan

Himpunan penyelesaian dari cos space open parentheses x plus 45 close parentheses degree plus cos space open parentheses x minus 45 degree close parentheses equals square root of 2 untuk 0 degree less than x less than 360 degree. Nilai sin space x equals...

  1. open curly brackets 0 degree comma 360 degree close curly brackets

  2. open curly brackets 45 degree close curly brackets

  3. open curly brackets 30 degree comma 330 degree close curly brackets

  4. open curly brackets 90 degree close curly brackets

  5. open curly brackets 180 degree close curly brackets

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A

Pembahasan

Ingat kembali:

cos space 45 degree equals sin space 45 degree equals 1 half square root of 2

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis A plus B right parenthesis end cell equals cell cos space A space cos space B minus sin space A space sin space B end cell row cell cos space left parenthesis A minus B right parenthesis end cell equals cell cos space A space cos space B plus sin space A space sin space B end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell cos space a comma space maka end cell row x equals cell plus-or-minus a plus k times 360 end cell end table 

 

Sehingga diperoleh perhitungan:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses x plus 45 close parentheses degree plus cos space open parentheses x minus 45 degree close parentheses end cell equals cell square root of 2 end cell row cell cos space x space cos space 45 minus sin space x space sin space 45 plus space cos space x space cos space 45 plus sin space x space sin space 45 end cell equals cell square root of 2 end cell row cell cos space x times space 1 half square root of 2 minus up diagonal strike sin space x times space 1 half square root of 2 end strike plus space cos space x times space 1 half square root of 2 plus up diagonal strike sin space x times space 1 half square root of 2 end strike end cell equals cell square root of 2 end cell row cell cos space x times space up diagonal strike square root of 2 end strike end cell equals cell up diagonal strike square root of 2 end strike end cell row cell cos space x end cell equals 1 row cell cos space x end cell equals cell cos space 0 end cell end table end style     

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell cos space 0 end cell row x equals cell plus-or-minus 0 plus k times 360 end cell row cell x subscript 1 end cell equals cell 0 plus open parentheses 0 close parentheses times 360 end cell row cell x subscript 1 end cell equals 0 row blank blank blank row cell x subscript 2 end cell equals cell 0 plus open parentheses 1 close parentheses times 360 end cell row cell x subscript 2 end cell equals 360 row blank blank blank end table

Dengan demikian, Himpunan penyelesaian dari persamaan tersebut adalah open curly brackets 0 degree comma space 360 degree close curly brackets

Jadi, jawaban yang tepat adalah A

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