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Pertanyaan

Tentukan HP setiap persamaan di bawah ini untuk interval open square brackets 0 degree comma space 360 degree close square brackets. Gunakan kalkulator jika diperlukan dan tuliskan jawabannya sampai ketelitian dua tempat desimal.

b. 16 space sin cubed space x minus 12 space sin squared space x plus 36 space sin space x minus 27 equals 0 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

 nilai HP yang memenuhi persamaan tersebut pada interval open square brackets 0 degree comma space 360 degree close square brackets adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank HP end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 48 comma 59 degree semicolon space 131 comma 41 degree close curly brackets end cell end table.

Pembahasan

Ingat bahwa:

  • sin space left parenthesis 180 minus x right parenthesis degree equals sin space x degree 
  • table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses x close parentheses end cell equals a row blank rightwards double arrow cell thin space x equals sin to the power of negative 1 end exponent open parentheses a close parentheses plus 360 degree n end cell row x equals cell 180 degree thin space minus sin to the power of negative 1 end exponent open parentheses a close parentheses plus 360 degree n end cell end table 

Sehingga, 

16 space sin cubed space x minus 12 space sin squared space x plus 36 space sin space x minus 27 equals 0

Misalkan sin open parentheses x close parentheses equals u

table attributes columnalign right center left columnspacing 0px end attributes row cell 16 u cubed minus 12 u squared plus 36 u minus 27 end cell equals 0 row cell open parentheses 16 u cubed minus 12 u squared close parentheses plus open parentheses 36 u minus 27 close parentheses end cell equals 0 row cell 9 open parentheses 4 u minus 3 close parentheses plus 4 u squared open parentheses 4 u minus 3 close parentheses end cell equals 0 row cell open parentheses 4 u minus 3 close parentheses open parentheses 4 u squared plus 9 close parentheses end cell equals 0 end table 

table row cell table attributes columnalign right center left columnspacing 0px end attributes row cell 4 u minus 3 end cell equals cell 0 space end cell row cell 4 u end cell equals 3 row u equals cell 3 over 4 end cell end table end cell row blank row cell atau thin space end cell row blank row cell 4 u squared plus 9 equals 0 space left parenthesis tidak space memenuhi right parenthesis end cell end table 

Substitusi ulang sin open parentheses x close parentheses equals u

sin open parentheses x close parentheses equals 3 over 4 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sin open parentheses x close parentheses equals 3 over 4 end cell row blank rightwards arrow cell x equals sin to the power of negative 1 end exponent open parentheses 3 over 4 close parentheses plus 360 degree n end cell row x equals cell 48 comma 59 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 48 comma 59 degree end cell row blank blank blank row blank rightwards arrow cell x equals 180 degree minus sin to the power of negative 1 end exponent open parentheses 3 over 4 close parentheses plus 360 degree n end cell row x equals cell 131 comma 41 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 131 comma 41 degree end cell end table 

Jadi, nilai HP yang memenuhi persamaan tersebut pada interval open square brackets 0 degree comma space 360 degree close square brackets adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank HP end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 48 comma 59 degree semicolon space 131 comma 41 degree close curly brackets end cell end table.

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