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Tentukan himpunan penyelesaian dari persamaan berikut untuk 0<x<2π cos(x+47​π)−cos(x−47​π)=1

Pertanyaan

Tentukan himpunan penyelesaian dari persamaan berikut untuk 0 less than x less than 2 straight pi

cos open parentheses straight x plus 7 over 4 straight pi close parentheses minus cos open parentheses straight x minus 7 over 4 straight pi close parentheses equals 1

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos open parentheses straight x plus 7 over 4 straight pi close parentheses minus cos open parentheses straight x minus 7 over 4 straight pi close parentheses end cell equals 1 row cell negative 2 sin space x times sin space 7 over 4 straight pi end cell equals 1 row cell negative 2 sin space straight x times open parentheses negative 1 half square root of 2 close parentheses end cell equals 1 row cell negative 2 sin space straight x end cell equals cell negative fraction numerator 2 over denominator square root of 2 end fraction end cell row cell sin space straight x end cell equals cell fraction numerator 1 over denominator square root of 2 end fraction end cell row cell sin space straight x end cell equals cell 1 half square root of 2 end cell row cell sin space x end cell equals cell sin space 1 fourth straight pi end cell end table

 

maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell 1 fourth straight pi plus n times 2 straight pi end cell row blank blank atau row cell x subscript 2 end cell equals cell open parentheses straight pi minus 1 fourth straight pi close parentheses plus n times 2 straight pi end cell row cell untuk space n end cell equals 0 row cell x subscript 1 end cell equals cell 1 fourth straight pi plus 0 times 2 straight pi end cell row blank equals cell 1 fourth straight pi end cell row cell x subscript 2 end cell equals cell open parentheses straight pi minus 1 fourth straight pi close parentheses plus 0 times 2 straight pi end cell row blank equals cell 3 over 4 straight pi space end cell row cell untuk space n end cell equals 1 row cell x subscript 1 end cell equals cell 1 fourth straight pi plus 1 times 2 straight pi end cell row blank equals cell 9 over 4 straight pi space left parenthesis tidak space memenuhi right parenthesis end cell row cell x subscript 2 end cell equals cell open parentheses straight pi minus 1 fourth straight pi close parentheses plus 1 times 2 straight pi end cell row blank equals cell 11 over 4 straight pi space left parenthesis tidak space memenuhi right parenthesis end cell end table

Dengan demikian, 

HP equals open curly brackets 1 fourth straight pi comma space 3 over 4 straight pi close curly brackets

107

5.0 (1 rating)

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